Characterization and Modeling of High Burn-Up Mixed Oxide Fuel

Home , Burnup

CHARACTERIZATION AND MODELING OF HIGH BURN-UP MIXED OXIDE FUEL

by Melissa Christine Teague A thesis submitted to the Faculty and the Board of Trustees of the Colorado School of

Mines in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Material

Science).

Golden, Colorado

Date ______

Signed:______Melissa C. Teague

Signed:______Dr. Jeffrey C. King Thesis Adviser

Signed:______Dr. Brian P. Gorman Thesis Adviser

Golden, Colorado Date______

Signed:______Dr. Brian P. Gorman Professor and Director Materials Science Program

Signed:______Dr. Michael J. Kaufman Professor and Head Department of Metallurgical and Materials Engineering

ABSTRACT Currently, fast reactor performance is largely constrained by the limitations of the materials involved in these reactors. The fuel is particularly limiting due to fission gas generation, changes in thermal conductivity, microstructure changes within the fuel, fuel swelling, and fuel-cladding chemical interaction (FCCI). Highly irradiated fuel is radially inhomogeneous in composition, microstructure, and temperature. In this work, high burn-up mixed oxide fuel with local burn-ups of 3.4-23.7% FIMA were destructively examined as part of a research project to understand the performance of oxide fuel at extreme burn-ups. Optical metallography, transmission electron microscopy and electron back-scatter diffraction were performed to further study the microstructure and chemical composition of the irradiated fuel. The optical micrographs were used to generate finite-element meshes in order to model the effective thermal conductivity of the irradiated fuel as a function of burn-up, radial position, and temperature.

The fuel-to-cladding gap closed significantly in samples with burn-ups below 7-9% FIMA. Samples with burn-ups in excess of 7-9% FIMA had a reopening of the fuel-to-cladding gap and evidence of joint oxide-gain formation. Additionally, high burn-up structure was observed in the two highest burn-up samples (23.7 and 21.3% FIMA). The microstructural modeling of the effective thermal conductivity found close (10-20%) agreement between the calculated effective thermal conductivities and the semi-empirical based analytical models, validating the finite- element mesoscale approach to microstructural modeling of effective thermal conductivities in irradiated fuel.

iii

TABLE OF CONTENTS

ABSTRACT ...... iii

LIST OF FIGURES ...... viii

LIST OF TABLES ...... xii

ACKNOWLEDGEMENTS ...... xiii

CHAPTER 1 GENERAL INTRODUCTION ...... 1

1.1 Introduction ...... 1

1.2 Dissertation Organization ...... 2

1.3 Literature Review...... 3

1.3.1 Irradiation Effects ...... 3

1.3.2 Fuel Composition Changes ...... 3

1.3.3 Microstructural Evolution during Irradiation ...... 6

1.4 Thermal Conductivity of Irradiated Oxide Fuels ...... 10

1.4.1 Unirradiated Thermal Conductivity of Oxide Fuels ...... 11

1.4.2 Thermal Conductivity Measurements ...... 13

1.4.3 Thermal Conductivity Modeling ...... 15

1.5 FFTF Fuel Background ...... 19

1.6 Sample Selection ...... 21

REFERENCES CITED ...... 26

CHAPTER 2 MICROSTRUCTURAL CHARACTERIZATION OF HIGH BURN-UP

MIXED OXIDE FAST REACTOR FUEL...... 31

2.1 Abstract ...... 31

2.2 Introduction ...... 31

iv 2.3 Design and Operation Conditions ...... 33

2.4 Experimental ...... 36

2.4.1 Sample Preparation ...... 36

2.4.2 Characterization ...... 37

2.5 Results and Discussion ...... 37

2.5.1 Microstructure Characterization ...... 38

2.5.2 Fuel-Cladding Gap Change ...... 43

2.6 Discussion ...... 44

2.7 Summary ...... 45

REFERENCES CITED ...... 45

CHAPTER 3 EBSD AND TEM CHARACTERIZATION OF HIGH BURN-UP MIXED

OXIDE FUEL ...... 48

3.1 Abstract ...... 48

3.2 Introduction ...... 48

3.3 Experimental Procedure ...... 50

3.3.1 Sample History/Background ...... 50

3.3.2 Sample Preparation ...... 50

3.4 Characterization ...... 52

3.5 Results ...... 52

3.5.1 TEM Results ...... 53

3.5.2 Characterization of cubes ...... 55

3.6 Conclusions ...... 56

3.7 Acknowledgements ...... 57

v REFERENCES CITED ...... 57

CHAPTER 4 MICROSTRUCTURAL MODELING OF THERMAL CONDUCTIVITY

OF HIGH BURN-UP MIXED OXIDE FUEL ...... 60

4.1 Abstract ...... 60

4.2 Introduction ...... 60

4.3 Background ...... 61

4.4 Sample History/Background ...... 65

4.5 Microstructural Modeling ...... 65

4.5.1 OOF Microstructure Reconstruction ...... 65

4.5.2 Microstructural Methods ...... 68

4.5.3 Microstructural Results ...... 71

4.5.4 Microstructural Discussion ...... 74

4.6 Pellet Scale Modeling ...... 74

4.6.1 Pellet Scale Methods ...... 74

4.6.2 Pellet Scale Results ...... 76

4.7 Conclusions ...... 79

4.8 Acknowledgements ...... 80

REFERENCES CITED ...... 80

CHAPTER 5 GENERAL CONCLUSION ...... 84

5.1 Conclusions ...... 84

5.2 Future Work ...... 86

Appendix A Permission to include Papers from Co-Authors ...... 87

Appendix B Mesh Sensitivity Study ...... 90

vi Appendix C Nomenclature and Acronyms ...... 94

vii

LIST OF FIGURES

Figure 1.1. Fission product yields for the fast neutron induced fission of uranium-235 [17]...... 4

Figure 1.2. Ellingham diagram of major fission products in oxide fuel [13]...... 5

Figure 1.3: a) as-sintered low magnification micrograph of annular MOX fuel pellet b) high

magnification micrograph showing bimodal pore size distribution in as-sintered fuel

pellet[5, 27]...... 7

Figure 1.4. Thermal restructuring in a 94% theoretical dense fast breeder reactor (U,Pu)O2

element showing the four microstructural regions: a) central void, b) columnar grains, c)

equiaxed, d) un-restructured [5]...... 8

Figure 1.5. Optical micrograph of high burn-up structure from the periphery of a fast breeder

reactor mixed oxide fuel pellet with a burn-up of 12% FIMA [7]...... 10

Figure 1.6: Thermal conductivity of (U,Pu0.15)O2-x as a function of temperature[39]...... 11

Figure 1.7. Comparison of thermal diffusivity versus burn-up for HBRP, NFIR, and PWR fuels

measured at 300°C [7]...... 14

Figure 1.8. Mesh creation in OOF2 [58]...... 18

Figure 1.10. Calculated axial burn-up profile for pins L01 and 150074...... 23

Figure 1.11. Calculated Centerline fuel temperature for 150074 and L01 at End of Life (EOL)

and Peak Power...... 24

Figure 2.1. Schematic of a nominal Core Demonstration Experiment fuel pin[19]...... 34

Figure 2.2. Linear heat rate of samples during course of irradiation...... 35

Figure 2.3. Drawing of stainless steel mount designed to reduce 2 mm thick cut slice to 1 mm

thickness...... 37

viii Figure 2.4. Optical micrographs of the transverse sections cut from FO-2 L01 and ACO-3

150074...... 38

Figure 2.5. Micrograph of sample 150074A with suspected grain pull-out circled...... 39

Figure 2.6. Radial cross-sections from FO-2 pin L01 taken at a) 40.1 cm b) 68.9 cm

and c) 89.1 cm from the bottom of the fuel column...... 40

Figure 2.7. Radial Cross-sections from ACO-3 pin 150074 taken at a) 40.1 cm b) 68.9 cm

and c) 89.1 cm from the bottom of the fuel column...... 42

Figure 3.1. Secondary electron SEM image of sample showing locations from which TEM and

cube samples were prepared...... 51

Figure 3.2. SEM images showing cube 3 prior to lift out with residual stress microcracking along

trenching a) and cube 3 after being mounted on the copper grid (b)...... 51

Figure 3.3. a) Stage/sample configuration during slicing of cube samples b) sample configuration

during EBSD/EDS scans...... 52

Figure 3.4. Bright field images of TEM sample 2 a) BF image showing precipitates and inset fuel

SADP b) BF image highlighting dislocation structure...... 54

Figure 3.5. Bright field images of TEM sample 3 a) BF image showing precipitates and grain

boundary with inset fuel SADP b) BF image highlighting dislocation structure...... 54

Figure 3.6. Bright field image of Mo-Ru-Rh-Pd-Tc precipitate in (U,Pu)O2 matrix in TEM

sample 3 b) indexed SADP from precipitate in image A...... 54

Figure 3.7. Phase maps of representative slices from a) cube 1 and b) cube 3...... 55

Figure 3.8. EBSD reconstructions of cubes 1 (a) and 3 (b) showing metallic precipitate

distribution within the cubes...... 56

Figure 4.1. Radial cross-section of sample ACO-3A with subsections used for modeling ...... 66

ix Figure 4.2. Radial optical micrographs of ACO-3B, FO-2B, and FO-2B used for mesh

generation...... 67

Figure 4.3. Mesh creation in OOF2 [19]...... 67

Figure 4.4. Effective thermal conductivity model, red is metallic precipitates, yellow porosity,

and fuel is light blue, enlarged region of mesh is shown to right to high light varying

element density to capture microstructure detail. The effective thermal conductivity of the

microstructure is calculated using equation 4.6...... 69

Figure 4.5. Graphs of effective thermal conductivity of microstructures in a) FO-2A and b)

FO-2B compared to analytical models...... 72

Figure 4.6. Graphs of effective thermal conductivity of microstructure in a) ACO-3A and b)

ACO-3B compared to analytical models...... 73

Figure 4.7. Geometry, materials, and typical mesh used for axisymmetric simulation of fuel

pellet temperature profile...... 75

Figure 4.8. Temperature profile for FO-2A and FO-2B calculated using the finite element

model...... 77

Figure 4.9. Comparison temperature profiles in pellets ACO-3A (left) and ACO-3B (right) with

CS2 MoO4 filling the gap and with gas filled gap...... 78

Figure A-1. Permission from Douglas Porter for publication...... 87

Figure A-2. Permission from Brandon Miller for publication...... 88

Figure A-3. Permission from Michael Tonks for publication...... 88

Figure A-4. Permission from Stephen Novascone for publication...... 89

Figure B-1. Micrograph from rim region of ACO-3A...... 91

x Figure B-2. Mesh of rim region in ACO-3A with homogeneity of 94%. Blue is fuel, yellow

porosity, and red is metal precipitates...... 91

Figure B-3. Mesh of rim region in ACO-3A with homogeneity of 97%. Blue is fuel, yellow

porosity, and red is metal precipitates...... 92

Figure B-4. Mesh of rim region in ACO-3A with homogeneity of 99%. Blue is fuel, yellow

porosity, and red is metal precipitates...... 92

LIST OF TABLES

Table 1.1. Groups of Fission Products[13]...... 5

Table 1.2. Design parameters of CDE fuel assemblies[68]...... 21

Table 1.3. Pins which were available for PIE...... 22

Table 1.4. Irradiation parameters of prepared fuel sections...... 25

Table 2.1. Design parameters of the CDE fuel assemblies...... 34

Table 2.2. Summary of irradiation history for metallographic samples...... 36

Table 2.3. Dimensions of FO-2 cross-sections before and after irradiation...... 40

Table 2.4. Dimensions of ACO-3 cross-sections before and after irradiation...... 43

Table 4.1. Irradiation history of fuel samples...... 65

Table 4.2. Polynomial fits to effective thermal conductivity for microstructures of the form

4 3 2 keff=AT +BT +CT +DT+E, where keff is effective thermal conductivity in W/m*K and T

is temperature in K...... 71

Table 4.3. Comparison of fuel centerline and surface temperatures in FO-2 samples from pellet

scale modeling using Duriez-NFI, Duriez-Lucuta, and radial dependent finite element

models...... 77

Table 4.4. Comparison of fuel centerline and surface temperature ...... 79

Table B-1. Properties of the tested meshes and the calculated effective thermal conductivity of

each mesh at 1000 K...... 93

xii

ACKNOWLEDGEMENTS I would like to thank my husband for his support and patience, and willingness to move across the country (twice) to support my achieving this degree. I want to thank my beautiful daughter, Mackenzie, though getting my PhD with an infant in tow has add some new challenges, you mean the world to me and I hope I can be a positive role model for you. Thank you to my mother, who believed in me, understood the pain of getting your PhD and inspired me to believe I could do it. I would also like to thank my first manager Don Burks for believing in me, taking chance on me, and pushing me out the door so I could get my PhD. Thank you to Department of Energy and Idaho National Laboratory for funding the work. I want to thank Steve Hayes for believing in me, and handing over amazing work for me to take on, and not laughing at optimism and naivety in how hard it is to get radiological work done. Thank you to the researchers who designed and irradiated the fuel samples that make up this work, little did they know the day that they were putting some of these samples into the reactor, I was being born. The fuel just had to wait awhile for me to make it to Idaho National Laboratory to do the work.

xiii CHAPTER 1

GENERAL INTRODUCTION

1.1 Introduction

The increasing demand for cost effective green energy has led to a renewed interest in nuclear energy, including the commercialization of sodium cooled fast reactors (SFRs) [1, 2]. In order for SFRs to become economically competitive with current light water reactors (LWRs) the average burn-up of fuel assemblies in an SFR will need to exceed ~150 GWd/tHM (~15% fissions per initial metal atom (FIMA))[3]. A secondary reason for interest in SFRs is their potential to “burn” or transmute long-lived transuranic isotopes contained in spent nuclear fuel produced by the current fleet of LWR[2, 4]. Currently, fast reactor performance is largely constrained by the limitations of the materials involved in the reactors, especially the metallic or mixed oxide ((U, Pu)O2) fuel itself. Problems include fission gas generation, changes in thermal conductivity, microstructure changes within the fuel, fuel swelling, and fuel cladding chemical interaction (FCCI)[5].

Being able to predict the operating temperatures of fuel in a nuclear reactor is critical to modeling fuel performance because it directly affects fission gas release, fission product migration, fuel plasticity and other important operating parameters [6]. The temperature at the cladding surface is well known and is equal to the coolant temperature plus the temperature rise over the oxide layers and fluid film; however, in order to determine the temperature profile within the fuel pellet, the thermal conductivity of the fuel must be known. Highly irradiated fuel is radially inhomogeneous in composition, microstructure, and temperature [5]. Compositional changes and micro-structural evolution make the evolution of thermal conductivity as a function of burn-up a complex problem which complicates calculation and modeling of the thermal conductivity [7]. Owing to the complex nature of the problem, most thermal conductivity models for irradiated fuel are empirically based, with limited applicability to designs outside the experimental space for which data exists [8]. The development for a more fundamentally based model will allow for the design of future fuels with reduced testing requirements [9-11].

The project increases the understanding of the effects of irradiation temperature and burn-up on the evolution of the microstructure, chemical composition, crystal structure, and

1 thermal conductivity in oxide fuel. A second goal of this work was to improve the existing models for thermal conductivity of high burn-up oxide fuel by precisely determining the chemical composition and crystal structure of high burn-up fuel. This information allowed the development of an improved, micro-scale finite-element based model of fuel thermal conductivity as a function of burn-up.

1.2 Dissertation Organization

This dissertation contains a collection of three papers submitted for publication in the Journal of Nuclear Materials. The three papers report the collection of work performed during this PhD. The first paper presents first of a kind optical microscopy on fuel with a wide range of burn-ups. The fuel rods were known to have performed well in reactor; however, the examination of the fuel allows for more detailed understanding of why the fuel performed better than expected. The second paper highlights the advanced technique development conducted to apply transmission electron microscopy (TEM) and electron backscatter diffraction ( EBSD) to highly irradiated fuel. Though the experimental data is limited at this time, and only provides a small snapshot into the fuel performance, the technique development provides the capability to revolutionize the characterization of irradiated fuel in the future. The third paper contains the results from integrating the optical micrographs, chemical data from EBSD/electron dispersive spectroscopy (EDS)/TEM, into thermal finite element models. Currently finite element modeling efforts treats the fuel as a homogenous material for simplicity, and lack of adequate data to do otherwise. My modeling efforts directly model the microstructures and phases present in the fuel, and are compared to the results from conventional models. The agreement between the models provides confidence in the microstructure based techniques, and can allow for future design work with radically different fuel microstructures to be performed and preliminarily tested.

Dr. Brian Gorman provided guidance and advice to the conduct of the microscopy work and data analysis pertaining to the work. Dr. Jeffrey King provided guidance on the nuclear impact of the work and data analysis help. Dr. Douglas Porter, a world leading fuel performance expert, provided discussion and guidance on performing post irradiation examinations and understanding historical data. Dr. Steven Hayes provided guidance and suggestions for modeling support, and provided training and help with running SAFE code calculations. Dr. Brandon Miller performed the TEM examination of the irradiated fuel and assisted with EDS analysis. Dr.

2 Michael Tonks provided help with development and data interpretation of the microstructural based models presented in Chapter 4, while Dr. Stephen Novascone provide help with development and data interpretation of pellet scale models.

1.3 Literature Review

The current state of research related to irradiation effects, thermal conductivity, and post irradiation exams is reviewed and summarized in this section. Background information on the test specimens considered in this project is also included in this section.

1.3.1 Irradiation Effects

Research and phenomena related to the effects of irradiation on the evolution of properties in oxide nuclear fuels are discussed in this section. The primary effects of irradiation on oxide fuels are compositional and microstructural changes.

1.3.1.1 Fuel Composition Changes A unique challenge to understanding irradiated nuclear fuel is the constantly changing chemical composition of the fuel itself. Unlike most materials, the chemical composition in irradiated nuclear fuel is constantly changing as uranium atom fission and the fission products decay. A prototypic fission product yield curve is presented in Figure 1.1. It can be seen that a wide range of elements is produced in fissioning fuel, which greatly complicates the understanding of fuel performance.

One of the most important fundamental questions about irradiated fuel is the chemical state of the fission products as a function of burn-up [12-14]. Widely accepted and verified burn-up codes, such as Oak Ridge Isotope Generation (ORIGEN), can accurately calculate the isotope/chemical composition of irradiated fuel based on its irradiation history [15]; however, the chemical structure or compounds which the fission products form are largely unknown. The chemical form and composition of the fission products within the fuel is critically important to both the mechanical and the thermal properties of the fuel. Additionally, knowing how fission products segregate within the fuel is necessary to predict whether or not cladding attack will be life limiting issue[16].

Figure 1.1. Fission product yields for the fast neutron induced fission of uranium-235 [17].

Fission products can be broken into four general categories based on the form they take in the fuel: volatile, metallic precipitates, ceramic precipitates, and oxides dissolved in the matrix [12]. Examples of each group are presented in Table 1.1. While some fission products, such as the rare earths, fall into a single category, others such as molybdenum can transition between forming metallic or oxide precipitates depending on the oxygen potential in the fuel [13, 18]. The oxygen potential generally remains constant or increases as burn-up increases[19]. Every time a uranium or plutonium atom fissions, two oxygen atoms are released. Initially the cladding and fission products tie up the excess oxygen; however, with increasing burn-up the sinks will be unable to sequester all of the oxygen and there will be net increase in free oxygen[19, 20]. Figure 1.2 presents an Ellingham diagram for the major fission products showing the oxygen affinity of key fission products. Fission products with high affinity for oxygen such as barium will stay in solid solution or precipitate as ceramics, while elements with lower affinity for oxygen such as ruthenium will form metallic precipitates.

As the fuels burn-up continues to increase, some elements such as zirconium reach their solubility limits, and have been found in ceramic precipitates[7, 21, 22]. The location of volatile fission products such as xenon, krypton, cesium, bromine, and iodine is an area of disagreement in the current literature [7, 12, 13, 21].

4 Table 1.1. Groups of Fission Products[13]. Fission Product Group Examples

Nd, Zr, Ce, Pu, Ba, La, Pr, Sr, Sm, Y, Rb, Te, Np, Solid Solution within the matrix Pm, Eu, Gd, Am, Th, Cm, Nb, Pa

Volatile Kr, Xe, Cs, Br, I

Ceramic Precipitates BaZrO3, SrZoO3, CsI, Cs2MoO4 Metallic Precipitates Mo, Ru, Tc, Rh, Te, Pd, Sn, Cd, Sb, Ag, In

Figure 1.2. Ellingham diagram of major fission products in oxide fuel [13].

5 Xenon and krypton are either found in dynamic solution within the matrix or in pores/bubbles[13]. Xenon and krypton are found in dynamic solid solution up to a saturation burn-up (~10% FIMA), at which point the gases precipitate out into pores[23]. Cesium, bromine, and iodine can be in solution, can be a liquid in pores, or form ceramic precipitates such as CsI and Cs2MoO4[24].

The non-soluble fission products form either ceramic or metallic precipitates[12]. Previous research has largely ignored the ceramic precipitates owing to the difficulty in identifying them in optical microscopy, and owing to their similarity to the oxide matrix phase dissolution behavior[13]. Many researchers have dismissed the ceramic precipitates as being unimportant, assuming that the properties of the precipitates would be similar to that of the matrix phase[24]. However, barium strontium molybdate, a ceramic precipitates found in high burn-up fuel, has been observed in two crystal structures ((Ba,Sr)MoO4 and/or (Ba,Sr)MoO3 [21]. The thermal conductivity of these two structures is different by an order of magnitude (3 versus 30 W/m-K, respectively), and thus the amount of (Ba,Sr)MoO3 present could have a large impact on the thermal conductivity of the fuel[21, 25].

Metallic precipitates have been extensively studied and are primarily composed of molybdenum and ruthenium, with lesser amounts of technetium, rhodium, and palladium [12, 13, 26]. The oxidation of molybdenum with the increasing oxygen potential in the fuel results in the concentration of molybdenum in the metallic precipitates decreasing as burn-up increases [13].

1.3.1.2 Microstructural Evolution during Irradiation The fast reactor fuel utilized in this study was manufactured using standard cold-pressing techniques. Prior to granulation 0.1 wt% Stereotex NF pore former was added to the powder. Granulation was achieved via pressing the powder to ~10 kpsi, followed by mechanical grinding. Following granulation 0.4-0.8 wt% Stereotex NF was added and the final pellets pressed to ~40 ksi. The resulting pellets had green densities of ~52% TD. The pellets were then sintered at 1690°C to ~92% TD (Figure 1.3a). The sintering is performed in flowing argon-8% hydrogen at

Figure 1.3: a) as-sintered low magnification micrograph of annular MOX fuel pellet b) high magnification micrograph showing bimodal pore size distribution in as-sintered fuel pellet[5, 27]. a flow rate of 6 cubic feet per hour. The use of pore formers results in a bimodal pore size distribution as seen in Figure 1.3b. The smaller sintering pores are thermally unstable in reactor, and densify early in life, while the larger pores formed by the pore former are stable during irradiation[5] The average grain size of the fuel pellets used in the FO-2 and ACO-3 assemblies was 10-15 µm.

Microstructural evolution of fast reactor oxide fuels under irradiation can be broken into two stages: initial restructuring upon reactor start-up resulting from thermal transport, and high burn-up, or “rim”, effects which typically occur at burn-ups in excess of ~70-80 GWd/tHM (gigawatt day/tone heavy metal) [5, 25]. The initial restructuring only occurs in fast reactor fuel regions with linear heat generation rates greater than 40 kW/m [5]. Heat generation rate directly correlates to temperature of the fuel; therefore, the higher the heat rate the higher the fuel temperature [5]. The thermally induced restructuring of MOX fuel in the Joyo reactor was almost complete after a 10 min irradiation [28]. Thermally induced restructuring results in the formation of four distinct regions within the fuel pellet: inner/central void, columnar grain region, equiaxed grain region, and an un-restructured region (see Figure 1.4).

Figure 1.4. Thermal restructuring in a 94% theoretical dense fast breeder reactor (U,Pu)O2 element showing the four microstructural regions: a) central void, b) columnar grains, c) equiaxed, d) un-restructured [5].

The central void (Figure 1.4a) is formed due to vapor transport of the central fuel to the outside cooler region or is present in the pellet from the beginning in annular fuel. The columnar grain region (Figure 1.4b) is made of large columnar grains with lenticular pores formed by vaporization of fuel from the hot (inner) side and then condensing on the cooler (outer) side of the pores [5]. The equiaxed grain region (Figure 1.4c) is the region where the temperature is sufficiently high to allow for grain growth via bulk diffusion, but too cool for vapor transport of fuel [5]. The outmost ring of fuel (Figure 1.4c) is too cool for grain growth to occur via bulk diffusion and remains unchanged during initial thermal restructuring [5]. The restructured microstructure of annular fuel pellets (such as the ACO-3 and FO-2 fuel samples of interest in the present research) is almost identical, except that the central void is present throughout the entire fuel column [29].

8 The second stage/category of microstructural evolution is the formation of a high burn-up, or rim-effect, microstructure that occurs at burn-ups in excess of ~70-80 GWd/tHM (7-8% FIMA) under certain conditions [25]. Experimenters first observed the high burn-up structure (HBS) (see Figure 1.5) in the late 1980’s as burn-ups were being pushed to new limits [30]. The HBS is defined by a porous region in which the pores are surrounded by round sub-grains, with the rest of the structure being made up of polyhedral sub-grains [25].

Currently, there is no consensus as to the exact mechanism(s) by which the HBS structure forms; however, a number of theories have been proposed [14, 23, 25, 31-33]. The three primary proposed mechanisms for HBS formation are recystrallization, recovery, or a combined recovery/recrystallization. The extremely limited experimental data has hampered the ability to conclusively determine the active mechanism[25] A primary unanswered question is whether the grain boundaries in the HBS region are low angle grain boundaries (indicating subdivisions of grains and recovery) or if they are high angle grain boundaries formed via polyganization/recrystallization, The grain boundary angle is debated due to conflicting grain boundary angle measurements made via TEM[25]. Ability to measure a significant number of grain boundaries using a technique such as EBSD would be invaluable to answering this question.

Although there is currently no comprehensive theoretical understanding of the formation of the HBS, experimental data has shown some general tends related to HBS formation [25, 32- 36]. Above 1000±150°C the HBS is not observed as the irradiation damage is thermally annealed/healed prior to inducing restructuring [37]. The minimum burn-up necessary for the formation of the HBS is typically between 70-80 GWd/tHM (~7-8%FIMA)[25, 31, 38]. Most of the work on the HBS has been focused on thermal reactor fuel; however, the same microstructure is seen in the periphery of SFR fuel at equivalent burn-up and temperature thresholds[25]. One of the complications in studying HBS formation in thermal reactor fuel is that both the temperature and burn-up vary across the pellet [31]. Two phenomena cause the burn-up variation in thermal reactor fuel: self-shielding and Pu breeding/fissioning.

Figure 1.5. Optical micrograph of high burn-up structure from the periphery of a fast breeder reactor mixed oxide fuel pellet with a burn-up of 12% FIMA [7].

The extremely high thermal fission cross section of 235U (~577 barns) means the neutrons are more likely to react with the periphery of the pellets, inducing fissioning and therefore higher burn-ups. The 238U in the periphery of thermal reactor fuel absorbs neutrons, converting to 239Pu and then fissioning.

The combination of these two phenomena results in the periphery of the pellet having ~2.5× the burn-up of the middle of the pellet [25]. As the temperature decrease towards the periphery of the fuel in thermal reactors, the burn-up increases. Fast reactor fuel has an even radial burn-up profile due to the lack of self-shielding, so temperature is the only variable across the periphery, potentially making it easier to determine the correlation between temperature, burn-up, and structure [25, 31].

1.4 Thermal Conductivity of Irradiated Oxide Fuels

Research related to the measurement and modeling of irradiated fuels is discussed in this section. Analytical and finite-element based modeling approaches are discussed.

10 1.4.1 Unirradiated Thermal Conductivity of Oxide Fuels

The most comprehensive measurements of the unirradiated thermal conductivity of mixed oxide fuel were performed by Duriez et al[39]. The thermal conductivity of MOX fuels with varying oxygen stoichiometry and plutonium contents were tested at temperatures up to 2300K, the results are presented in Figure 1.6.

(U,Pu)O2 is an insulating ceramic, whose heat transport at temperatures below ~1400 K is dominated by phonon transport. The thermal conductivity of the (U,Pu)O2 matrix phase can be described using the following equation for phonon transport dominated regimes [39, 40]:

(1.1)

Where kph=thermal conductivity in phonon regime, A=coefficient representing the concentration of phonon scattering centers, B=intrinsic thermal resistivity of the lattice resulting from scattering of phonons.

Figure 1.6: Thermal conductivity of (U,Pu0.15)O2-x as a function of temperature[39].

11 The A coefficient is the sum of the thermal resistances due to the scattering of phonons induced by individual point defects such as interstitial atoms, impurities, vacancies, and dislocations and can be stated as [41]:

(1.2)

V=mean atomic volume lattice, ν=mean phonon velocity, θD=Debye Temperature, h=planks constant, Γi=phonon scattering by point defect

The total scattering coefficient due to defects can be approximated as [39]:

(1.3)

Γi=phonon scattering by point defect, xi=atomic fraction point defect, Mi=atomic weight of point defect, ri=atomic radius of point defect, ε=32(1+1.6γ),γ=Gruneisen constant

The coefficient B represents the intrinsic lattice thermal resistivity due to phonon-phonon scattering and can be represented by the following simplified model[39].

(1.4)

γ=Gruneisen Constant h=Planks constant k=Boltzmann’s Constant =mean atomic volume lattice, =mean atomic mass, θD=Debye Temperature

Duriez et al. assumed the A and B coefficients were independent of plutonium content and calculated the following correlations for A and B as a function of oxygen stoichiometry[39].

(1.5)

(1.6)

Where x=oxygen stoichiometry shift

12 Duriez et al. then used the measured conductivity data at high temperatures with the phonon contribution subtracted to develop an analytical fit to the data above 1400 K[39]

(1.7)

9 where kht=thermal conductivity in high temperature range C=1.689x10 WK/m and D=13520K

Combination of the phonon regime (Equation 1.1) and high temperature regime (Equation 1.7) results in an equation to describe the thermal conductivity over the entire temperature regime[39]

(1.8)

1.4.2 Thermal Conductivity Measurements

Despite thermal conductivity being one of the most important properties of irradiated fuel, only a few example of experimentally determined thermal conductivity exist after over 40 years of study [7, 24, 42-46]. The available thermal conductivity data for irradiated nuclear fuel can be broken into two categories: thermal conductivities indirectly inferred from centerline fuel temperature measurements, and direct thermal conductivity measurements made on out-of-pile fuel samples [7, 9, 39, 46-49]. Indirectly measured data requires assumptions about the gap width and gap conductance, and averages the effective thermal conductivity over the entire pellet, which may not be uniform [7]. There are two main disadvantages with thermal conductivity data measured out-of-pile: the data does not represent the significant temperature gradient across the fuel during irradiation, and it does not incorporate the potential effects of the massive amount of transient damage induced within the fuel during the fission process [7].

For the purpose of developing a more fundamental based thermal conductivity model, out-of-pile data allows for the isolation of more variables, such as burn-up and temperature, than do in-pile measurements. Out-of-pile measurements can be further subdivided into measurements of reactor fuel irradiated under normal operating conditions and measurements of disc fuel samples irradiated under special controlled conditions [7, 24, 37]. The High Burn-up

13 Rim Project (HBRP) and the Nuclear Fuel Industry Research (NFIR) project irradiated thin wafers of fuel between metal plates that ensured a uniform temperature and burn-up profile across the samples [44, 45]. Recent extensive out-of-pile testing on pressurized water reactor (PWR) fuel at burn-ups up to 100 GWd/tHM provided comparisons to the currently available thermal conductivity data for high burn-up fuel[7]. These tests used a modified laser flash method capable of using irregularly shaped samples to measure the thermal diffusivity of oxide fuel with an average burn-up of 102 GWd/tHM, with a peak radial burn-up of ~250 GWd/tHM at temperatures up to 837°C [7]. The data from disc fuel samples are valuable in understanding the separate effects on fuel conductivity; however, since fuel in operational reactors has a steep temperature (and burn-up in LWR) gradient, the microstructure and chemical inventory in traditional reactor fuels will be different [7]. Thermal diffusivity data obtained from disc fuel and PWR fuel experiments are compared in Figure 1.7. There is good agreement between the disc and PWR fuel diffusivity toward the periphery of the PWR fuel where the irradiation temperature was similar to that of the disc fuel; however, at the center of the PWR fuel the temperatures were higher than that of the disc fuel leading to a different microstructure and a considerably higher thermal diffusivity (Figure 1.7). The data clearly shows that irradiation temperature along with burn-up impacts the thermal diffusivity of irradiated fuel [7].

Figure 1.7. Comparison of thermal diffusivity versus burn-up for HBRP, NFIR, and PWR fuels measured at 300°C [7].

14 1.4.3 Thermal Conductivity Modeling

Analytical and computational approaches to modeling the thermal conductivity of irradiated oxide fuels are described in sections 1.4.3.1 and 1.4.3.2, respectively.

1.4.3.1 Analytical Modeling Efforts FRAPCON-3 is the standard code for modeling high burn-up fuel performance for nuclear regulatory commission (NRC) reactor licensing [8]. The most recent version of FRAPCON-3 contains the Duriez-Modified Nuclear Fuel Industries (NFI) model [39]. This model uses measurements from un-irradiated MOX fuel pellets and burn-up degradation functions based on

UO2 data to empirically predict the thermal conductivity of MOX fuel pellets in LWRs up to 62 GWd/tHM [8, 39, 50]. The model is strictly empirical and is only licensed for modeling fuel for which testing has been performed [8]. Additionally, the use of UO2 data for the burn-up degradation of MOX fuel results in an uncertainty of ±15-20% [8, 39]. The Duriez-NFI model along with the degradation terms are shown in equations 1.9-1.12.

(1.9)

(1.10)

(1.11)

(1.12)

Where Keff is effective thermal conductivity of fuel, x is amount off stoichiometry, T is temperature in kelvin, β is burn-up in % FIMA, f(β) is a term accounting for dissolved fission products, g(β) is a term accounting for radiation damage generation, h(T) is a term accounting for radiation damage annealing.

Another widely used model is the Duriez-Lucuta model. In the model the Duriez unirradiated thermal conductivity is then modified by a series of multiplier: dissolved fission products (Fd), porosity (Fb), precipitated fission products (Fp) and radiation damage (Fr) as outlined in detail by Lucuta et al.[7, 11] and shown in equations 1.13-1.17.

15 (1.13)

(1.14)

(1.15)

(1.16)

(1.17)

Where β is the burn-up in % FIMA, T is temperature in kelvin, and ρ is the percent porosity.

The dissolved fission product term is based on the measured degradation of fission products in SIMFUEL, and takes into account the effect of all fission products that are incorporated into the fluorite matrix, including fission gas atoms[9]. The dissolved fission products reduce the conductivity in the phonon-transport regime by acting as phonon scattering sites and increasing the A coefficient in equation 1.1[39] The precipitated fission products term, Fp, is based the assumption of metallic precipitates forming within the grains and on grain boundaries and is treated using a modified Klemens’ perturbation factor to incorporate increased precipitates as a function of burn-up[9, 51]. A key assumption in the calculation of both precipitated and dissolved fission products is the chemical state that the fission products are in, which the model uses unirradiated SIMFUEL to estimate; however, extensive chemical characterization of irradiated fuel would eliminate the assumptions of using simulated fuel from the model. The porosity term, Fb, is the Maxwell-Eucken equation effect of porosity where the pores have much lower conductivity than the matrix phase. The thermal transport within the pores is assumed to be via radiation only, which may be conservative based on the high pressures thought to be present in the pores of the HBS regions[7, 9, 52] Lucuta acknowledges that the Fb term is a crude simplification of the complex situation of porosities effect on thermal conductivity in oxide fuel; however, for simplicity it is utilized. Since porosity is inhomogeneous throughout the pellets and evolves with burn-up the Fb term is typically only used to account for initial pellet porosity[50]. Increasing the amount of data on porosity at high burn-ups and its distribution throughout the matrix, as performed in this thesis, will help to understand how applicable this

16 simplification is to high burn-up fuel. The discrete modeling of porosity including the true shape and size distribution discussed in chapter 4 provides direct comparison of this simplification to real microstructures. The radiation damage term is derived from an empirical fit to reduction in thermal conductivity of UO2 early in life due to radiation damage. There is no dependence on burn-up since the effect of radiation damage saturated early in life for oxide fuel [9, 50]

1.4.3.2 Finite Element Analysis Based Modeling Efforts The second approach to modeling the thermal conductivity of irradiated oxide fuel is to use finite element analysis (FEA) techniques to model the impact of various parameters such as porosity, precipitates, and microstructure[53]. Computer based FEA modeling is a relatively new field, which is growing based on the availability of increasing computing power/capability [54]. Bakker et al. performed a series of 2D and 3D FEA studies to determine the effect of radiation heat transfer across pores on the overall thermal conductivity of irradiated UO2 fuel [55, 56]. They then compared the results to various analytical models for similar phenomena[56]. The FEA models were in agreement with accepted analytical models; however, both the FEA models created/used by Bakker et al., and the analytical models which they compared their results to, are based on idealized microstructures. Thus, these results are of limited applicability to real microstructures [55, 56]. Realizing the shortcomings of these idealized models, modelers including Bakker et al. have begun to incorporate more realistic microstructure and phase information into models [53, 57]. Historically, this was a time consuming process, as real microstructures had to be manually digitized to create meshes for importation into FEA solvers [53, 55, 57].

The need for a more automated means by which to create mesh models of real microstructures gave rise to OOF2 (Object Oriented Finite element analysis version 2), a freeware program created and supported by the National Institute of Standards and Technology (NIST) [58, 59]. Complex real micrographs with multiple phases can be imported into OOF2 and then converted into computational meshes for FEA modeling[58]. The basic process is outlined in Figure 1.8. Initially a uniform mesh made of elements (in this examples triangles) is overlaid on the micrograph (Figure 1.8a) followed by annealing/refinement steps. The goal of annealing steps is to increase the homogeneity of each element. OOF2 defines the homogeneity, E, of an element using equations 1.18-1.20 [58]

17 (1.18)

(1.19)

(1.20)

α=tunable parameter between 0-1, T=triangle/element, ai(T)=fraction of elements composed of pixel set i, N=number of pixel categories, AT=area of element, LT=perimeter of element

The annealing steps are performed by a Monte Carlo algorithm where elements are moved at random and the changes are kept if the resulting element is more homogeneous than the previous element [58]. Figure 1.8b show an example mesh after 10 annealing iterations.

Figure 1.8. Mesh creation in OOF2 [58].

18 Elements whose E is greater than a specified value (in this case 0.3) are then divided in half (Figure 1.8c) and further annealing steps are performed (Figure 1.8d).

Utilizing microstructure based meshes versus homogenized until cells, or meshed based off of idealized microstructures, greatly increases the accuracy of FEA models for heat transport across microstructures[60]. Additionally, microstructure based models of complex microstructures provide better agreement with experimental data for thermal and mechanical properties than either idealized FEM or analytical model [58, 60-66].

1.5 FFTF Fuel Background

Extensive fast reactor fuel development programs were carried out in the US, Russia, France, and Japan with the resultant research efforts peaking in the early 1980’s [2]. Much of this work came to an abrupt halt by the mid 1990’s, with the exception of limited fuel development work that continued in Japan and France [67]. Currently, there are no operating fast spectrum reactors in the US, making the examination of historically irradiated fast reactor fuel especially important to determine fundamental fuel performance of mixed oxide (MOX) fuel [4].

The core demonstration experiments (CDE) fuel tests conducted in the fast flux test facility (FFTF) in the early to mid-1990s are of particular interest to the development and understanding of mixed oxide fuel performance and behavior under irradiation[68]. The CDE tests were intended to demonstrate an economically viable fast reactor fuel design. Fuel pins from sub-assemblies FO-2 and ACO-31 are available for post irradiation examinations (PIE). These pins represent some of the highest burn-ups ever achieved in prototypic fast reactor fuel. The pins available for examination have fuel sections ranging in burn-up from ~3-23% FIMA. The CDE experiments were terminated before any significant PIE was performed, providing a unique opportunity to learn about the fuel performance of mixed oxide fuel without the expense and time commitment of performing an irradiation test [4, 29, 68-70].

A schematic of a CDE fuel pin is presented in Figure 1.9 showing the configuration and nominal, as built, data for the CDE experiments. The FO-2 and ACO-3 sub-assemblies each

1 The significance/meaning of the assembly identifiers FO-2 and ACO-3 have not been located in the historical literature, it is possible that they were randomly assigned identifiers.

19 contain 169 HT-9 clad pins which are 238 cm long (Figure 1.9). In both FO-2 and ACO-3 the fueled region is a 91.44 cm stack of annular type (U,Pu)O2 pellets that have 92% theoretical density (see Figure 1.9). There are a few slight differences between the two fuel assemblies: FO-2 has slightly larger pellets (5.59 mm OD vs. 5.55 mm OD for ACO-3), the pellet smear density is 80% for FO-2 versus 84% for ACO-3, and the Pu enrichment in FO-2 is 26% versus 29% in ACO-3. The fuel stack is sandwiched between two 16.5 cm blanket stacks of annular depleted uranium oxide fuel pellets[68]. The detailed as built data for FO-2 and ACO-3 sub-assemblies is presented in Table 1.2.

FO-2 was irradiated for 311.8 Equivalent Full Power Days (EFPD) to a peak burn-up of 62.6 GWd/tHM (~6 %FIMA) and a peak fast (E>0.1 MeV) fluence of 9.9x1022 n/cm2. ACO-3 was ACO-3 was irradiated for 1524.2 EFPD to a peak burn-up of 231.5 GWd/tHM (~23 %FIMA) and a peak fast (E>0.1 MeV) fluence of 38.93x1022 n/cm2

Figure 1.9. Schematic of a nominal core demonstration experiment fuel rod[68].

20 Table 1.2. Design parameters of CDE fuel assemblies[68]. Design Parameter FO-2 ACO-3 Number of Pins 169 169 Cladding Material HT-9 HT-9 Outer diameter (mm) 6.858 6.858 Wall Thickness (mm) 0.559 0.559 Plenum volume (cm3) 23.6 23.6 Wire wrap Material HT-9 HT-9 Diameter (mm) 1.359 1.361 Pitch (cm) 15.24 15.24 Fuel Pellet Material MOX MOX Geometry Annular Annular outer diameter (mm) 5.59 5.55 Inner diameter (mm) 1.397 1.473 Smeared density (%TD) 80 84 Pellet density (%TD) 91.7 92 Oxygen-to-metal ratio 1.955 1.95 Fuel composition (Pu/(Pu+U)) (wt%) 26 29 Duct Material HT-9 HT-9

1.6 Sample Selection

A total of 10 pins from the ACO-3 sub-assembly and two pins from the FO-2 sub-assembly were available for examination in this PhD project (Table 1.3). All ten ACO-3 pins have similar irradiation histories, as do the two FO-2 fuel pins. Non-destructive exams were performed on all twelve available pins. Resource limitations and a desire to retain irradiated pin for future testing in Transient Reactor Test Facility (TREAT) limited destructive exams to only one pin from each sub-assembly (see Table 1.3).

21 Table 1.3. Pins which were available for PIE. Examinations Pin No. Sub-Assembly to be Performed 150019 ACO-3 Non-destructive 150100 ACO-3 Non-destructive 150103 ACO-3 Non-destructive 150086 ACO-3 Non-destructive 150089 ACO-3 Non-destructive 150092 ACO-3 Non-destructive 150074 ACO-3 Destructive 150059 ACO-3 Non-destructive 150061 ACO-3 Non-destructive 150171 ACO-3 Non-destructive L01 FO-2 Destructive K01 FO-2 Non-destructive

Pin 150074 from ACO-3 was a part of a cluster of three pins that were directly next to each other during irradiation; therefore, performing destructive exams on pin 150074 provided valuable data for future destructive exams of the sister pins. There is historic non-destructive exam data performed in 1987 available for pin L01 which allowed comparison between historic and current PIE capabilities.

One of the primary goals for this PhD research was to understand the evolution of microstructure and properties in uranium oxide fuel as a function of temperature and burn-up. Resource constraints limited examination to three sections per fuel rod. In order determine where to section the fuel pins to get the largest range of irradiation temperatures and burn-ups, the fuel temperatures during irradiation were calculated.

The fuel performance code SAFE, developed at Argonne National Laboratory-West in the 1990s [71], calculated the thermal parameters for L01 and 150074 at various points in the pins irradiation history (beginning of life, peak power, and end of life). SAFE is a 2D FORTRAN code that uses as-built dimensional data, unirradiated thermal conductivities, linear heat generation rates, and coolant flow information to perform basic heat transfer calculations for

22 scoping studies. The code was developed to provide a fast way to perform thermal analysis on proposed experiments going into reactor. It provides a rough estimation of fuel temperatures for determining sample cutting locations. Figure 1.10 and 1.11 present the calculated axial burn-up profile and calculated centerline temperature for the FO-2 and ACO-3 fuel pins.

Using the axial burn-up profiles along with the calculated irradiation temperatures sections were selected to be cut at 45.7, 68.6, and 91.4 cm with respect to the bottom of the fuel column from both L01 and 150074 (the locations of the sections are marked by red dotted lines in Figure 1.10 and Figure 1.11). Table 1.4 summarizes the key irradiation parameters (burn-up, peak centerline temperature, and end of life centerline temperature) for the 150074 and L01 fuel pins.

Figure 1.10. Calculated axial burn-up profile for pins L01 and 150074.

Figure 1.11. Calculated Centerline fuel temperature for 150074 and L01 at End of Life (EOL) and Peak Power.

24 Table 1.4. Irradiation parameters of prepared fuel sections. FO-2 Sample ID L01A L01B L01C Distance from Bottom of Fuel Column (cm) 40.1 68.9 89.1 BOL EOL BOL EOL BOL EOL Burn -up (FIMA EOL) 6.7 6.7 5.8 5.8 3.4 3.4 Fuel Center(°C) 2108 2206 1978 2091 1504 1675 Fuel Surface (°C) 969 1079 978 1077 891 979 Clad Surface (°C) 485 467 563 540 610 592

ACO- 3 Sample ID 150074A 150074B 150074C Distance from Bottom of Fuel Column (cm) 40.1 68.9 89.1 BOL EOL BOL EOL BOL EOL Burn -up (FIMA EOL) 23.7 23.7 21.3 21.3 13.7 13.7 Fuel Center(°C) 1735 1281 1665 1221 1265 993 Fuel Surface (°C) 847 813 872 809 792 737 Clad Surface (°C) 460 416 530 468 574 488

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30 CHAPTER 2

MICROSTRUCTURAL CHARACTERIZATION OF HIGH BURN-UP MIXED OXIDE FAST REACTOR FUEL

A paper submitted to the Journal of Nuclear Materials

Melissa Teague, Douglas Porter, Steven Hayes, Idaho National Laboratory

Brian Gorman, Jeffrey King, Colorado School of Mines

2.1 Abstract

High burn-up mixed oxide fuel with local burn-ups of 3.4-23.7% FIMA (fissions per initial metal atom) were destructively examined as part of a research project to understand the performance of oxide fuel at extreme burn-ups. Optical metallography of fuel cross-sections measured the fuel-to-cladding gap, clad thickness, and central void evolution in the samples. The fuel-to-cladding gap closed significantly in samples with burn-ups below 7-9% FIMA. Samples with burn-ups in excess of 7-9% FIMA had a reopening of the fuel-to-cladding gap and evidence of joint oxide-gain (JOG) formation. Additionally, high burn-up structure (HBS) was observed in the two highest burn-up samples (23.7 and 21.3% FIMA). The HBS layers were found to be 3-5 times thicker than the layers found in typical LWR fuel. The results of the study indicate that formation of JOG and or HBS prevents any significant fuel-cladding mechanical interaction from occurring, thereby extending the potential life of the fuel elements.

2.2 Introduction

The increasing demand for cost effective green energy has led to a renewed interest in nuclear energy, including the commercialization of sodium-cooled fast reactors (SBRs)[1, 2]. In order for SBRs to become economically competitive with current light water reactors (LWRs), the average burn-up of fuel assemblies in an SBR will need to exceed ~150 gigawatt days/ton heavy metal (GWd/tHM) (~15% fissions per initial metal atom [FIMA])[3]. A secondary reason for interest in SBR, is their potential to transmute the long-lived transuranic isotopes contained in the spent nuclear fuel produced by the current fleet of LWRs[2, 4]. Currently, fast reactor performance is largely defined by the limitations of the materials involved in these reactors.

Particularly limiting is the fuel, whether it is metallic or mixed oxide ((U, Pu)O2). Fission gas

31 generation, changes in thermal conductivity, microstructure changes within the fuel, fuel swelling, and fuel-cladding chemical interaction (FCCI)[5] all contribute to the problem. Qualifying a stainless steel cladding material to the desired conditions of high operating temperatures and large plenum gas pressures, while having that alloy be resistant to void swelling at high neutron exposures, is also a challenge.

The ability to predict the operating temperatures of fuel in a nuclear reactor is critical to modeling fuel performance, since it strongly affects fission gas release, fission product migration, fuel plasticity and other important operating parameters [6]. A critical component to accurately predicting the operating temperature of the fuel is the continuous evolution of the size and composition of the fuel-cladding gap. Early in life oxide fuel swells to close the as-fabricated gap and fuel temperatures decrease. At greater than 7-9% FIMA burn-up, the gap reopens to the original gap size[7-9]. Previous research on SBR oxide fuel has suggested the reopening of the gap coincides with the exodus of cesium and molybdenum from the fuel matrix, and the formation of a cesium molybdate phase in the gap (referred to as joint oxide-gain [JOG]), and the release of fission gas from the matrix[7, 8, 10-12]. At similar burn-ups (~7-9% FIMA and above) and at fuel temperatures below 1000°C, formation of the high burn-up structure (HBS) has been documented in both SBR and LWR fuels[8, 10-13]. The high burn-up structure is characterized by a porous region in which the pores are surrounded by round sub-grains, with the rest of the structure being made up of polyhedral sub-grains[13]. Currently, there is no consensus as to the exact mechanism(s) by which the HBS structure forms or how it may affect fuel performance[13-18]. While JOG formation has not been documented in LWR fuel, SBR fuels have frequently exhibited this phenomenon. Portions of SBR fuels that were operating above 1000°C when reaching 7-9% FIMA burn-up resulted in JOG formation without an accompanying HBS[8]. Due to limited available data, it is unclear how JOG formation and high burn-up structures are related and if they occur concurrently in SBR fuel with burn-up at or above 7-9% FIMA.

Currently there are no operating fast spectrum reactors in the US, making the examination of legacy fuels previously irradiated in fast reactors particularly important in the effort to determine the fundamental fuel performance characteristics of mixed oxide (MOX) fuel[4]. The pins examined in this paper have fuel sections ranging in burn-up from ~3-23% FIMA. These

32 fuel pins represent some of the highest burn-ups ever achieved in prototypic fast reactor fuel pins[7-12]. The wide range of burn-ups present in these samples provides a unique opportunity for studying fuel performance throughout life[8, 10, 11].

This research focused on the use of optical microscopy to study the evolution of the fuel-cladding gap, JOG formation, and fuel microstructure as a function of burn-up and axial location within the fuel column, along with a comparison to previously published data.

2.3 Design and Operation Conditions

The Core Demonstration Experiment (CDE) fuel tests conducted in the Fast Flux Test Facility (FFTF) in the mid-1980s to early-1990s are of particular interest to the development and understanding of mixed oxide fuel performance and behavior under irradiation[19]. The CDE tests were intended to demonstrate an economically viable fast reactor fuel design. The CDE experiments were terminated before any significant post irradiation examinations (PIE) were performed. Fuel pins from CDE sub-assemblies FO-2 and ACO-3 were still intact and retrievable from storage, providing a unique opportunity to learn about the fuel performance of mixed oxide fuel without the expense and time commitment of performing a new irradiation test[4, 19-22]. Preliminary PIE results were previously published for FO-2 along with some limited non-destructive exams on ACO-3[23]. These preliminary results show that the fuel performed well beyond the design limit (~1500 Effective Full Power Days (EFPD) versus design goal of 1000 EFPD) without any major degradation.

Figure 2.1 presents a schematic of a CDE fuel pin showing the configuration and nominal as-built data for the CDE experiments. The FO-2 and ACO-3 sub-assemblies each contained 169 pins clad in HT-9 steel that are 238 cm long. In both FO-2 and ACO-3 the fueled region is a

91.44 cm stack of annular type (U,Pu)O2 pellets sintered to 92% theoretical density (see Figure 2.1). There are a few slight differences between the two fuel assemblies: FO-2 has slightly larger pellets (5.59 mm OD vs. 5.55 mm OD for ACO-3), the fuel-cladding gap is 205 and 190 μm for FO-2 and ACO-3, respectively, and the Pu enrichment in FO-2 is 26% versus 29% in ACO-3. The fuel stack is sandwiched between two 16.5 cm blanket stacks of annular depleted uranium oxide fuel pellets[19]. Detailed design parameter data for FO-2 and ACO-3 sub-assemblies is presented in Table 2.1.

Figure 2.1. Schematic of a nominal Core Demonstration Experiment fuel pin[19].

Table 2.1. Design parameters of the CDE fuel assemblies. Design Parameter FO-2 ACO-3 Number of Pins 169 169 Cladding Material HT-9 HT-9 Outer diameter (mm) 6.858 6.858 Wall Thickness (mm) 0.533 0.559 Fuel Pellet Material MOX MOX Geometry Annular Annular Outer diameter (mm) 5.59 5.55 Inner diameter (mm) 1.397 1.473 Fuel-to-Cladding Gap (μm) 101 95 Blanket-to-Cladding Gap (μm) 305 340 Smeared density (%TD) 80 76.1 Pellet density (%TD) 91.7 93 Oxygen-to-metal ratio 1.96 1.95 Fuel composition (Pu/(Pu+U)) (wt%) 26 29 Duct Material HT-9 HT-9

Figure 2.2. Linear heat rate of samples during course of irradiation.

The FO-2 fuel sub-assembly was irradiated between December 22, 1984 and April 25, 1986 to a peak burn-up of ~6% FIMA and a peak fast fluence of 9.9 × 1022 n/cm2 (E>0.1 MeV). The ACO-3 assembly was irradiated between Aug. 17th, 1985 and March 13th, 1992 to a peak burn-up of ~23 % FIMA and a peak fast fluence of 38.9×1022 n/cm2 (E>0.1 MeV). The linear heat generation rate over the life of the assemblies can be seen in Figure 2.2.

FO-2 pin L01 and ACO-3 pin 150074 were selected for sectioning and metallographic examination. The fuel centerline, fuel surface, and cladding surface temperatures during irradiation of pins L01 and 150074 were estimated using the thermal analysis code SAFE, developed at Argonne National Laboratory-West in the 1990s[23, 24]. For end of life estimates the fuel-cladding gap of ACO-3 pin 150074 was assumed to be filled with Cs2MoO4 based on previously examined high burn-up fuel [7]. Table 2.2 shows the thermal conditions of the prepared metallographic samples during the peak power cycle and at end-of-life (EOL).

35 Table 2.2. Summary of irradiation history for metallographic samples. FO-2 Sample ID L01A L01B L01C Distance from Bottom of Fuel Column (cm) 40.1 68.9 89.1 BOL EOL BOL EOL BOL EOL Burn-up (FIMA EOL) 6.7 6.7 5.8 5.8 3.4 3.4 Fuel Center(°C) 2108 2206 1978 2091 1504 1675 Fuel Surface (°C) 969 1079 978 1077 891 979 Clad Surface (°C) 485 467 563 540 610 592

ACO- 3 Sample ID 150074A 150074B 150074C Distance from Bottom of Fuel Column (cm) 40.1 68.9 89.1 BOL EOL BOL EOL BOL EOL Burn-up (FIMA EOL) 23.7 23.7 21.3 21.3 13.7 13.7 Fuel Center(°C) 1735 1281 1665 1221 1265 993 Fuel Surface (°C) 847 813 872 809 792 737 Clad Surface (°C) 460 416 530 468 574 488

2.4 Experimental

The methods utilized for the preparing the irradiated fuel samples for analysis along with details concerning how the samples were characterized are outlined in this section. Additionally, information on the software and methods for analyzing the results are presented.

2.4.1 Sample Preparation

Sample preparation for the optical metallographic mounts was carried out at the Idaho National Laboratory in the Hot Fuel Examination Facility (HFEF) in a controlled dry argon atmosphere. A Struers slow speed saw was used to cut 2-3 mm thick slices at 40.1, 68.9, and 89.1 cm from the bottom of the fuel column in pins L01 and 150074..

Figure 2.3. Drawing of stainless steel mount designed to reduce 2 mm thick cut slice to 1 mm thickness.

The slices were then placed in specially designed stainless steel metallurgical mounts (Figure 2.3) and back-potted with epoxy. The mounts were then ground until the inner metal ring was removed, resulting in a 1 mm thick slice of the fuel remaining. Thinning the sample to 1 mm was necessary to reduce the radioactive dose from the sample for future out- of-cell characterization. After grinding to final thickness, the samples were vacuum back-potted again to help prevent pullout and breakage of the delicate fuel. The final step polished the sample to a 0.25 micron finish using diamond pastes.

2.4.2 Characterization

Prepared metallographic mounts were imaged using a Leitz MM5RT metallograph located inside a nitrogen filled hot cell at HFEF. Full cross-section composite images were obtained at 50x magnification. Higher magnification micrographs (100-500x) were collected for quantitative metallographic analysis across the radius of the fuel specimens. Image analysis was performed using the commercially available software ImageJ (NIST).

2.5 Results and Discussion

This section discusses the results obtained from the characterization of the high burn-up fuel samples including microstructural changes and fuel-to-cladding gap analysis. The results are compared to previous literature results, and their significance and importance are explained.

37 2.5.1 Microstructure Characterization

The effect of temperature and burn-up on microstructure was investigated using the optical micrographs of the samples. Low magnification (50x) full cross-section composite images of the prepared samples are shown in Figure 2.4 along with the location from which the samples were prepared. Some of the samples showed signs of suspected grain pullout during polishing (Figure 2.5). Grain pullout is suspected due to the atypical size and angularity of the dark area. Grain pullout is not unexpected as a consequence of the amount of porosity and the highly friable nature of irradiated fuel[15, 25]. More suspected grain pullout was observed in the center columnar regions of the fuel than in the equiaxed rim regions. This finding is in contrast to most ceramics where high aspect ratio grains, such as what is observed in the columnar grain regions, show more resistance to pullout[26]. The grain pullout in the columnar grain region may be enhanced by the lenticular pores also present in these regions. It is suspected that individual fuel grains are pulling out, leaving the appearance of greater porosity in the microstructure. Due to the suspected pullout quantitative porosity measurements from the micrographs was not possible.

Figure 2.4. Optical micrographs of the transverse sections cut from FO-2 L01 and ACO-3 150074.

Figure 2.5. Micrograph of sample 150074A with suspected grain pull-out circled.

2.5.1.1 Results from FO-2 L01 Figure 2.6 shows radial cross-sections from the L01 pin. Samples L01A and L01B show the typical fuel restructuring found in fast reactor fuel pins operated at linear powers over 35 kW/m[5]. The central portion of the fuel pellets display columnar grains and pores, a middle region with equiaxed grains, and a rim region with an as-sintered grain structure. The radial variation in microstructure is due to the temperature gradient of the fuel pellet during irradiation[5]. Sample L01C showed little change in microstructure from as-fabricated due to the lower fuel temperature and burn-up relative to the top of the fuel column. The 50x composite images (Figure 2.4) were used to measure the cladding thickness, central void diameter, and fuel-cladding gap dimensions. Table 2.3 compares these measurements to as-built data. The measured cladding thickness of L01A and L01B are within the as-fabricated range, and the smooth interior of the cladding indicated no signs of fuel-cladding chemical interaction. The measured cladding thickness of L01C (0.573±0.015mm) is larger than the as-fabricated thickness of 0.531 mm, while the outer diameter of the pin remains within 0.2% of the as fabricated dimensions Table 2.3.

Figure 2.6. Radial cross-sections from FO-2 pin L01 taken at a) 40.1 cm b) 68.9 cm and c) 89.1 cm from the bottom of the fuel column.

Table 2.3. Dimensions of FO-2 cross-sections before and after irradiation. As-Fabricated L01A L01B LO1C Pin OD 6.858 6.871±0.0076 6.873±0.0076 6.871±0.0076 (mm) Central Void 1.372 1.872±0.0430 1.875±0.062 1.365±0.0178 (mm) Gap (μm) 116.2 70.0±30.8 91.9±24.5 55.7±16.9 Cladding Thickness 0.531 0.546±0.019 0.512±0.018 0.573±0.015 (mm)

Swelling in excess of 0.2% in HT-9 has not been previously observed, making this measurement suspect. One possibility is that there is a reaction phase in the gap that cannot be distinguished from the cladding in optical microscopy. The roughness of the inner surface of the cladding (Figure 2.4) also suggests a reaction layer is present. Further examination using an

40 elemental analysis mapping technique such as wavelength-dispersive spectroscopy or energy-dispersive spectroscopy, or etching of the cladding to expose more features in optical microscopy, would be required to determine if a reaction layer is present or if the cladding has truly swelled inward. The central voids in L01A and L02B increased by 69.9% and 60.9%, respectively; this increase in central void diameter is consistent with previous results for SBR annular MOX fuel that has undergone restructuring[5]. The central void in L01C remained unchanged from the as-fabricated dimensions.

2.5.1.2 Results from ACO-3 150074 The radial cross-sections from the ACO-3 pin 150074 can be seen in Figure 2.7. Sample 150074C shows no signs of microstructural change from its as-fabricated condition, which is expected due to the low temperatures (below 2000 K) it experienced at the top of the fuel column [5]. Samples 150074A and 150074B show a fully restructured microstructure with the formation of HBS on the periphery of the pellet. The thickness of the HBS region is 499 ± 17 μm and 528 ± 33 μm in 150074A and 150074B, respectively. The formation of the HBS in SBR fuel has been reported previously; however, the similarities and connections with the HBS structure in LWR fuel have been largely neglected[13, 15, 25]. The exact mechanism by which HBS structure is formed in either LWR or SBR fuel is still not fully understood; however, it is believed to be primarily an irradiation damage induced change that is independent of chemical composition or starting microstructure[13, 17, 18, 27-29]. The HBS structure forms in both LWR and SBR fuel at burn-ups of 7-9% FIMA and at similar upper limits on temperature of ~1000°C; however, the bubble and grain size observed in SBR fuel HBS are slightly larger than those typically reported for LWR HBS[13]. The width of the HBS structure observed in 150074A and 150074B is also significantly larger than that observed in LWR fuels (<200 μm)[13, 15, 25]. There are two primary differences between the parameters in LWR and SBR fuels during HBS structure formation: temperature and burn-up profiles. In LWR fuel the typical fuel surface temperature is ~350°C, compared to ~650°C in SBR fuel[5]. Another significant difference is the sharp burn-up gradient in LWR fuel pellet rim due to self-shielding affects that lead to enhanced plutonium production and fissioning at the periphery of the fuel. These phenomena result in the periphery of the pellet having ~2.5x the burn-up as the center[13, 15].

Figure 2.7. Radial Cross-sections from ACO-3 pin 150074 taken at a) 40.1 cm b) 68.9 cm and c) 89.1 cm from the bottom of the fuel column.

Fast reactor fuel has an essentially uniform radial burn-up profile due to the long mean free path of fast neutrons, so temperature is the only variable across the periphery[5]. The larger width of the HBS region in SBR fuel could allow for future characterization/experimentation techniques that require larger samples sizes (e.g., micro-mechanical testing) to be performed on the HBS structure.

The 50x composite images were also used to measure the cladding thickness, central void, and fuel -cladding gap dimensions of the ACO-3 150074 cross-sections, which are compared to the as-fabricated values in Table 2.4. Samples 150074A and 150074B showed a reduction in cladding thickness. The observed cladding creep (diameter increase) in 150074A and 150074B is responsible for 0.87% and 0.62% reductions in wall thickness in the pins (Figure 2.4). The remaining wall thinning is potentially due to FCCI; however, further examination would be required to determine if wastage from FCCI has in fact occurred. The cladding thickness in sample 150074C increased to 0.6221 ± 0.04211 mm; as discussed earlier (Section 2.9.2), HT9 swelling under these conditions is suspect, especially by this amount. The inner surface of the cladding in 150074C is also very irregular (Figure 2.4), suggesting a reaction layer that is not

42 distinguishable from the cladding in optical microscopy. The peak in diametric strain was observed near the top of the fuel, similar to that seen previously for ACO-1 pins and correlated to an increase in Cs activity[19]. This is caused by a fuel/Cs reaction, the product of which involves a volume increase which stresses the cladding and this product could be what is appearing as a cladding thickness increase. The central void diameter increased from 1.397 mm to 1.700 mm and 1.547 mm in 150074A and 150074B, respectively, in agreement with published SBR annular MOX fuel behavior[5, 19]. The central void in sample 150074C decreased by 61.7%; this significant closing of the central void without a creeping down of the outer fuel pellet suggests fuel migration axially up the fuel column. Previously published data on high burn-up annular MOX SBR fuel pins did not show similar closing of the annular void at the top of the fuel column[7-11].

2.5.2 Fuel-Cladding Gap Change

Due to the fuel loss during sample preparation and the asymmetric nature of the prepared fuel pin cross-sections, quantifying the widths of the fuel-cladding gaps was difficult. Thirty-six measurements were made utilizing a uniform radial grid overlay with lines every 10 degrees on the micrographs. The average and standard deviation are reported in Table 2.3 and Table 2.4. Closure of the fuel-cladding gap at these burn-ups (6.7%, 5.8%, and 3.4% FIMA) is well documented in SBR oxide fuel, resulting from fuel swelling caused by solid and gaseous fission products in solution with the matrix[8, 9].

Table 2.4. Dimensions of ACO-3 cross-sections before and after irradiation.

As-Fabricated 150074A 150074B 150074C Pin OD 6.847 6.899 ± 0.0076 6.883 ± 0.0076 6.922 ± 0.0076 (mm) Central Void 1.397 1.700 ± 0.039 1.547 ± 0.035 0.534 ± 0.021 (mm) Gap (μm) 97.8 202.1 ± 37.4 203.0 ± 44.3 115.1 ± 44.6 Cladding Thickness 0.5575 0.535 ± 0.008 0.508 ± 0.011 0.622 ± 0.042 (mm)

43 The fuel-cladding gap has reopened in the ACO-3 samples 1500074A, 150074B, and 150074C to an average of 202.1 ± 37.4 μm, 203.0 ± 44.3 μm, and 115.1 ± 44.9 μm, respectively. The reopening of the fuel-cladding gap has been observed in other SBR fuel at burn-ups in excess of 7-9%FIMA[7-11]. The reopening of the gap has been shown to occur with the formation of JOG in the gap[7-11]. Because of the hydroscopic nature of the JOG compounds, they are not retained in the cross-sections examined, which were prepared using a water-based polishing medium. However, previously published data strongly indicates that JOG was likely present in the fuel-cladding gap of 150074A and 150074B[7-11]. Previously published calculations show the minimal strain (1.2% or less) measured in ACO-3 pins in the fuel column region is due only to HT-9 creep from fission gas pressure, suggesting that JOG mitigates the fuel-cladding mechanical interaction (FCMI)[7-11, 23].

2.6 Discussion

The mechanism by which JOG occurs is not fully understood; however, JOG has been observed over the entire length of fuel columns at a wide variety of temperatures indicating that its minimum formation temperature is less than that experienced in typical SBR MOX pins. The potential connection between JOG and HBS formation cannot be clearly determined from current experimental data. Both JOG and HBS formation have a similar threshold burn-up requirement (7-9 % FIMA); however, HBS formation only occurs in fuels operated below 1000°C, while JOG formation occurs across the entire operating temperature spectrum. The upper temperature limit of HBS formation indicates that radiation damage is the dominant factor in HBS formation, since above this temperature the damage is annealed out faster than it is imparted. The lack of an upper temperature limit for JOG suggests that it is driven primarily by fission product concentrations. HBS has been observed without JOG in LWR fuel, and JOG without the formation of HBS in fuel below 1000°C (such as in sample 150074C), which suggests that the two mechanisms are independent of each other despite their similar threshold burn-up requirements. The formation of JOG is still a poorly understood phenomenon in large part due to the lack of sufficient experimental data. Due to the difficulty in retaining the JOG phase during sample preparation, it is possible that other researchers have missed its presence. Specifically in LWR fuel, where another phenomena is observed called cladding lift out. At high burn-ups (>7- 9% FIMA), they observe the cladding moving away from the fuel. Due to the water based

44 sample preparation techniques used, it is possible that the cladding is not moving away from the fuel but that the fuel is shrinking and the gap is being filled with a JOG compound. Cladding lift off is a considered a limiting condition in LWR fuel due to the assumed poor heat transfer across this gap, if it were found to be filled with a solid phase it could greatly extend the life of current LWR fuel.

2.7 Summary

Optical microscopy has been performed on samples prepared from HT-9 clad annular MOX fuel pins irradiated to peak burn-ups of 6.7 and 23.7% FIMA in the fast flux test facility. The samples examined had local burn-ups ranging from 3.4-23.7% FIMA. The microscopy measured the fuel-cladding gap, cladding thickness, and central void dimensions in the samples. The fuel-cladding gap closed significantly in samples with burn-ups below 7-9% FIMA due to fuel swelling; while, the samples with burn-ups in excess of 7-9% FIMA showed a reopening of the fuel-cladding gap and evidence of joint oxide-gain formation. The two highest burn-up samples (23.7 and 21.3% FIMA) also exhibited high burn-up structure formation. The high burn-up structure layer in the fast breeder reactor pins was ~500 μm thick; roughly 3-5 times as thick as the high burn-up structure observed in light water reactor fuel pellets. The formation of joint oxide-gain and/or high burn-up structure in the high burn-up samples apparently mitigates any significant fuel cladding mechanical interaction from occurring, thereby extending the potential life of the fuel pins.

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47 CHAPTER 3

EBSD AND TEM CHARACTERIZATION OF HIGH BURN-UP MIXED OXIDE FUEL

A paper submitted to the Journal of Nuclear Materials

Melissa Teague, Brandon Miller, Idaho National Laboratory

Brian Gorman, Jeffrey King, Colorado School of Mines

3.1 Abstract

Understanding and studying the irradiation behavior of high burn-up oxide fuel is critical to licensing of future fast breeder reactors. Advancements in experimental techniques and equipment are allowing for new insights into previously irradiated samples. In this work dual column focused ion beam (FIB) / scanning electron microscope (SEM) was utilized to prepare transmission electron microscope samples from mixed oxide fuel with a burn-up of 6.7% FIMA. Utilizing the FIB/SEM for preparation resulted in samples with a dose rate of <0.5 mRem/hr compared to ~1.1 R/hr for a traditionally prepared transmission electron microscope (TEM) sample. The TEM analysis showed that the sample taken from the cooler rim region of the fuel pellet had ~2.5× higher dislocation density than that of the sample taken from the mid-radius due to the lower irradiation temperature of the rim. The dual column FIB/SEM was additionally used to prepare and serially slice ~25 micron cubes. High quality electron back scatter diffraction (EBSD) were collected from the face at each step, showing, for the first time, the ability to obtain EBSD data from high activity irradiated fuel.

3.2 Introduction

Fast breeder reactor (FBR) research is a key component in closing the nuclear fuel cycle both in the United States and abroad. The United States, Russia, France, and Japan carried out extensive fast reactor fuel development programs with the resultant research efforts peaking in the early 1980s[1, 2]. Much of this work came to an abrupt halt by the mid-1990s, with the exception of limited fuel development work that continued in Japan and France[3]. Currently, there are no operating fast spectrum reactors in the US, making the examination of historically irradiated fast reactor fuel especially important to determine fundamental fuel performance parameters of mixed oxide (MOX) fuel[4].

48 Studying irradiated fuel is greatly complicated by the difficult nature of working with radioactive samples[5-7]. Advances in characterization techniques and equipment are revolutionizing the ability to study materials and are currently widely applied to other material science problems; however, the expense and difficulty of working with radiological samples has often lead to delays in the application of these advanced technologies to radioactive materials[5, 8, 9]. Two prevalent techniques that have experienced limited to no application in irradiated fuel work are transmission electron microscopy (TEM) and electron backscatter diffraction (EBSD). TEM and EBSD both require precise sample preparation, which can be difficult even using non-activated materials[10, 11]. Irradiated oxide fuels present an exceptional challenge in sample preparation as the material is very brittle, porous, multiphase, and highly radioactive. There are only limited TEM studies on irradiated fuel available in the literature, and no EBSD studies have been published on irradiated oxide fuel[12-18].

The development of focused ion beam (FIB) instruments in the late 1990s enabled the preparation of TEM and EBSD samples that were previously very difficult or even impossible to obtain by traditional means[19-25]. Due to the expense of FIB instruments and the risk of internal contamination that would make non-radiological work on the instrument more difficult, researchers have been hesitant to implement these techniques on highly radioactive materials. Although examinations of unirradiated fuel and activated metals have been previously demonstrated[26, 27], work on irradiated fuel has not been reported. This work expands on previous efforts and demonstrates site-specific FIB specimen preparation techniques for TEM and EBSD from irradiated oxide fuel.

Additionally, FIB prepared TEM samples have greatly reduced specimen mass, which for irradiated materials, reduces the radiation emitted from the sample making working with the sample easier and safer. A traditional 3 mm TEM sample is over three million times larger by mass than a TEM lamellae prepared via FIB (15μm × 15μm × 100 nm). As dose rate is proportional to the mass of the specimen, the present technique yields a tremendous advantage for research on radioactive materials. The calculated dose rate from a traditional TEM lamella of the irradiated fuel material considered in this study was ~1.1 R/hr contact compared to ~3.5×10-8 R/hr for the FIB prepared samples. This allows for greater access to research facilities and equipment for research as a result of the decreased hazard to both the operator and equipment.

49 The FIB allows for preparation of irradiated fuel surfaces for EBSD that are virtually impossible to achieve with mechanical in-cell polishing techniques. In-situ FIB polishing with an EBSD detector additionally allows for an experimental approach, where the sample is polished and tested until an acceptable EBSD pattern can be obtained[28]. This allows for repeated polishing tests without having to repeatedly handle the radioactive sample. The FIB also allows for the preparation of small (25 micron) cubes from the irradiated fuel sample which can then be successively sliced and scanned to provide 3D microstructure and compositional information[29]. The three dimensional structure of irradiated fuels is largely unknown, and a limiting factor in being able accurately model the thermal behavior of the fuel.

This study illustrates the successful implementation of FIB techniques to prepare TEM and EBSD samples from highly irradiated oxide fuels to determine radial changes in microstructure and chemistry.

3.3 Experimental Procedure

The samples history and irradiation parameters are given in this section. The methods utilized for the preparing the irradiated fuel samples for analysis along with details concerning how the samples were characterized are outlined in this section. Additionally, information on the software and methods for analyzing the results are presented.

3.3.1 Sample History/Background

Fuel samples analyzed in this work were irradiated in the Fast Flux Test Facility (FFTF, Idaho National Laboratory) in the mid-1980s. The fuel sample came from the FO-2 fuel assembly and is an annular MOX fuel pellet with HT-9 cladding. The analyzed sample was sectioned from the mid-plane of the fuel column, had a burn-up of 6.7% FIMA, and reached a calculated peak centerline temperature during irradiation of 2462°C. A more detailed irradiation history has been previously submitted by Teague et al.[30].

3.3.2 Sample Preparation

Samples were prepared and analyzed using a FIB/SEM instrument (FEI Co. Quanta 600, Eindhoven, Netherlands) at Idaho National Laboratory. TEM lamellae and block samples were taken from three radial locations within the fuel to obtain samples with a variety of irradiation

50 temperatures from the locations of which are shown in Figure 3.1. The TEM samples were fabricated using standard in-situ lift out techniques described elsewhere[25]. Nominal 25 micron cubes were prepared following the procedure outlined by Schaffer and Wagner, and welded onto a standard copper half grid[29]. Figure 3.2a shows the cube prepared at location 3 (Figure 3.1) after milling but prior to lift-out. Figure 3.2b illustrates the cube mounted on a copper grid.

Figure 3.1. Secondary electron SEM image of sample showing locations from which TEM and cube samples were prepared.

Figure 3.2. SEM images showing cube 3 prior to lift out with residual stress microcracking along trenching a) and cube 3 after being mounted on the copper grid (b).

51 3.4 Characterization

All TEM work was performed on a JEOL 2010 TEM equipped with an Oxford Instruments (Concord, MA, USA) EDS system located at Idaho National Laboratory. Analysis was performed on lamellae taken from location 2 and 3 (Figure 3.1). Bright field imaging highlighted the microstructural features within the samples. Selected area diffraction patterns were collected from the fuel and precipitates. EDS point scans and maps were also collected from the samples to aid in identification of the composition of the precipitates and bulk grains.

The prepared cubes were loaded onto a 45° pre-tilted holder in the FIB. The sample was tilted 7° for ion milling (Figure 3.3a) and the sample was then rotated 180° and tilted 25° for EBSD/EDS data collection (Figure 3.3b). The EBSD (EDAX DigiView IV, Draper, UT, USA) scan used a step size of 0.2 microns and an accelerating voltage of 20 keV. The EDS (EDAX Apollo X SDD) scan performed concurrently mapped Pu, U, O, Mo, Ru, Rh, Cs, Ba, and Sr. Following the acquisition of the EBSD/EDS scan, a 300 nm layer was removed from the cube face and the scans repeated. A total of twenty scans were collected for each cube, resulting in a studied volume of 25×25×6 microns. The cube prepared from location 2 in Figure 3.1 was found to be a single grain; therefore, the analysis from this cube is not reported.

3.5 Results

This section discusses the results obtained from the characterization of the high burn-up fuel samples including TEM, EBSD and EDS analysis.

Figure 3.3. a) Stage/sample configuration during slicing of cube samples b) sample configuration during EBSD/EDS scans.

52 3.5.1 TEM Results

The effect of radial position on the structure and composition of the fuel was studied using TEM samples prepared from locations 2 and 3 (Figure 3.1). TEM sample 2 was found to contain a single grain of (U,Pu)O2 with small intragranular five metal alloy precipitates containing Mo-Pd-Ru-Rh-Tc (Figure 3.4). Selected area diffraction patterns were obtained from the fuel in sample 2 and indexed as cubic (U,Pu)O2 (Figure 3.4); unfortunately, the metal precipitates were too small to obtain indexable selected area diffraction patterns (SADP). The average max Ferret’s diameter of the observed metallic precipitates was 105±28 nm, as measured using ImageJ (National Institute of Health, Bethesda, MD).

Sample 3 contained three (U,Pu)O2 grains with both inter and intragranular five metal precipitates (Figure 3.5a). The precipitates in sample 3 had an average max Ferret’s diameter of 339 ± 84 nm. The larger precipitates in sample 3 allowed for diffraction patterns to be collected and which indexed as hexagonal space group P63/mmc (Figure 3.6), consistent with previously observed metallic alloy precipitates in irradiated oxide fuel[31, 32].

Bright field images highlighting the dislocation structure of the samples can be seen in Figure 3.5b and Figure 3.6. The dislocation density in the two samples was calculated using the random line method proposed by Ham et al. and a lamellae thickness of 75 nm was used for the density calculations[33]. The density of dislocations in samples 2 and 3 were found to be 1.13×10-18/cm2 and 2.75×10-18/cm2. The radiation damage rate is constant across the radius of fast reactor fuel; however, the temperature at position two is approximately 500°C hotter than position three. The higher irradiation temperature in location three acted to anneal more of the irradiation damage resulting in sample 2 having ~2.5x lower dislocation density than sample 3.

The higher dislocation density in sample 3 indicates higher damage to the area, which is consistent with the micro-cracking during cube sample preparation at site 3 that was not observed at site 2 (Figure 3.2). The increased residual damage in the periphery of the pellet is theorized to play a key role in high burn-up structure formation[34].

Figure 3.4. Bright field images of TEM sample 2 a) BF image showing precipitates and inset fuel SADP b) BF image highlighting dislocation structure.

Figure 3.5. Bright field images of TEM sample 3 a) BF image showing precipitates and grain boundary with inset fuel SADP b) BF image highlighting dislocation structure.

Figure 3.6. Bright field image of Mo-Ru-Rh-Pd-Tc precipitate in (U,Pu)O2 matrix in TEM sample 3 b) indexed SADP from precipitate in image A.

54 3.5.2 Characterization of cubes

Cubes with nominal dimensions of 25 μm were successfully prepared and removed from a bulk irradiated MOX sample. The small mass and subsequent small activity of the cubes allowed for EDS and EBSD analysis without flooding of the detectors by background radiation. Additionally, the small cubes allowed for serial sectioning and reconstruction of the 3D microstructure of the material without additional sample handling.

Phase maps of representative slices from cube 1 and 3 are shown in Figure 3.7. The phase maps show a matrix of (U,Pu)O2 grains with secondary five metal (Mo-Pd-Ru-Rh-Tc) precipitates. A significant finding of this work is that high quality EBSD patterns were able to be collected from the irradiated fuel despite the background gamma and beta radiation and large amount of radiation damage to the fuel. The twenty EBSD scans of each cube were reconstructed into 3-D volumes using commercially available software (Avizo Fire 7.0, VSG-3D Inc, Figure 3.8).A clear difference in the metal precipitate structure can be seen in the two cubes.

Figure 3.7. Phase maps of representative slices from a) cube 1 and b) cube 3.

Figure 3.8. EBSD reconstructions of cubes 1 (a) and 3 (b) showing metallic precipitate distribution within the cubes.

Cube 1 contains two large precipitates located on the grain boundary, while cube 3 shows smaller inter- and intra-granular precipitates evenly distributed through the volume. Larger inter-granular precipitates are expected in cube 1 due to it having an end of life temperature ~1000°C higher than in cube 2, in agreement with optical microscopy results[30]. 3.6 Conclusions

A dual column FIB / SEM was successfully used to prepare high quality TEM and cube EBSD/EDS samples from high burn-up MOX fuel. The prepared TEM samples, due to their small mass, had significantly reduced dose rate compared to traditionally prepared TEM samples (1.1 R/hr vs. 3.5×10-8 R/hr respectively), thus reducing the hazards of working with them. The prepared TEM samples were of high enough quality to image the extensive dislocation networks present in the fuel matrix, and to collect high quality selected area diffraction patterns. Cubes from the bulk MOX sample were effectively prepared and serial sectioned using the FIB. High quality EBSD patterns were obtained from the cube faces, showing, for the first time, the ability to obtain EBSD data from high activity irradiated fuel.

TEM and EBSD examination of the prepared samples gave insight into the effect of radial position in the fuel pellet on structure and composition of the samples. The TEM sample from the cooler rim region of the pellet was found to have ~2.5x higher dislocation density than that of

56 the sample taken from the mid-radius due to the lower irradiation temperature at the rim. The characterization of the fuel cubes showed that the sample from near the central void had large inter-granular metal precipitates, while the sample from the rim contained small inter- and intra-granular precipitates. The application of FIB to sample preparation of highly radioactive samples, such as irradiated fuel, enables first of a kind application of cutting edge characterization techniques to study the evolution of microstructure and chemistry in fuel as a function of irradiation. This fundamental characterization of irradiated fuel is critical to developing a microstructural understanding of nuclear fuel performance.

3.7 Acknowledgements

The authors would like to thank Jim Madden of Idaho National Laboratory and Jessica Riesterer of FEI for assistance with FIB sample preparation and characterization. This work was funded by the Department of Energy Fuel Cycle and Research Development program and the INL Laboratory Directed Research & Development (LDRD) Program. This manuscript has been authored by Battelle Energy Alliance, LLC under Contract No DE-AC07-05ID14517 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United Sates Government retains a nonexclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow other to do so, for the United States Government purposes.

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57 8. Kleykamp, H. and R. Pejsa, X-ray diffraction studies on irradiated nuclear fuels. Journal of Nuclear Materials, 1984. 124: p. 56-63. 9. Bagger, C., M. Mogensen, and C.T. Walker, Temperature measurements in high-burnup UO2 nuclear fuel: implications for thermal conductivity, grain growth and gas release. Journal of Nuclear Materials, 1994. 211(1): p. 11-29. 10. Ayache, J., et al., Sample Preparation Handbook for Transmission Electron Microsocpy. 2010, New York, NY: Springer. 338. 11. Barna, A. Low Angle and Low Energy ion Beam Etching for TEM Sample Preparation. in Multinational Congress on Electorn Microscopy. 1997. Portoroz, Slovenia. 12. Matzke, H. and J. Spino, Formation of the rim structure in high burnup fuel. Journal of Nuclear Materials, 1997. 248: p. 170-179. 13. Nogita, K. and K. Une, High resolution TEM of high burnup UO2 fuel. Journal of Nuclear Materials, 1997. 250(2,3): p. 244-249. 14. Nogita, K. and K. Une, Formation of pellet-cladding bonding layer in high burnup BWR fuels. Journal of Nuclear Science and Technology, 1997. 34(7): p. 679-686. 15. Nogita, K. and K. Une, Irradiation-induced recrystallization in high-burnup UO2 fuel. Journal of Nuclear Materials, 1995. 226(3): p. 302-10. 16. Nogita, K., K. Une, and Y. Korei, TEM analysis of pellet-cladding bonding layer in high burnup BWR fuel. Nuclear Instruments & Methods in Physics Research, Section B: Beam Interactions with Materials and Atoms, 1996. 116(1-4): p. 521-526. 17. Ray, I.L.F., et al., An electron microscopy study of the RIM structure of a UO2 fuel with a high burnup of 7.9% FIMA. Journal of Nuclear Materials, 1997. 245(2,3): p. 115-123. 18. Ray, I.L.F., H. Thiele, and H. Matzke, Transmission electron microscopy study of fission product behavior in high burnup uranium dioxide. Journal of Nuclear Materials, 1992. 188: p. 90-5. 19. Steer, T.J., et al., 3-D focused ion beam mapping of nanoindentation zones in a Cu–Ti multilayered coating. Thin Solid Films, 2002. 413(1–2): p. 147-154. 20. Sakamoto, T., et al., Development of an Ion and Electron Dual Focused Beam Apparatus for Three-Dimensional Microanalysis. Japanese Journal of Applied Physics, 1998. 37(Part 1, No. 4A): p. 2051-2056. 21. Dunn, D.N. and R. Hull, Reconstruction of three-dimensional chemistry and geometry using focused ion beam microscopy. Applied Physics Letters, 1999. 75(21): p. 3414-3416. 22. Phaneuf, M.W., Applications of focused ion beam microscopy to materials science specimens. Micron, 1999. 30(3): p. 277-288. 23. Inkson, B.J., M. Mulvihill, and G. Möbus, 3D determination of grain shape in a FeAl-based nanocomposite by 3D FIB tomography. Scripta Materialia, 2001. 45(7): p. 753-758. 24. Inkson, B.J., et al., Subsurface nanoindentation deformation of Cu–Al multilayers mapped in 3D by focused ion beam microscopy. Journal of Microscopy, 2001. 201(2): p. 256-269. 25. Giannuzzi, L.A. and F.A. Stevie, A review of focused ion beam milling techniques for TEM specimen preparation. Micron, 1999. 30(3): p. 197-204.

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59 CHAPTER 4

MICROSTRUCTURAL MODELING OF THERMAL CONDUCTIVITY OF HIGH BURN-UP MIXED OXIDE FUEL

A paper accepted in the Journal of Nuclear Materials

Melissa Teague, Michael Tonks, Stephen Novascone, Steven Hayes, Idaho National Laboratory

4.1 Abstract

Predicting the thermal conductivity of oxide fuels as a function of burn-up and temperature is vitally important to efficient and safe operation of nuclear reactors. However, modeling the thermal conductivity of fuel is greatly complicated by the radially inhomogeneous nature of irradiated fuel in both composition and microstructure. In this work, radially and temperature-dependent models for effective thermal conductivity were developed utilizing optical micrographs of high burn-up fuel. The optical micrographs were employed to create finite element meshes with the OOF2 software. The meshes were then used to calculate the effective thermal conductivity of the microstructures using Idaho National Laboratory’s BISON [1] fuel performance code. The new thermal conductivity models were utilized to calculate thermal profiles at end of life for the fuel pellets. These results were compared to thermal conductivity models from the literature, and comparison between the new finite element-based thermal conductivity model and the Duriez-Lucuta model was favorable.

4.2 Introduction

The ability to predict the operating temperature of fuel in a nuclear reactor is critical to modeling fuel performance because it directly affects fission gas release, fission product migration, fuel plasticity and other important operating parameters [2]. In order to determine the temperature profile within the fuel pellet, the thermal conductivity of the fuel must be known. However, highly-irradiated fuel is radially inhomogeneous in both composition and microstructure [3]. Compositional changes and microstructural evolution during reactor operation make the evolution of thermal conductivity as a function of burn-up a complex problem, which complicates calculation and modeling of the temperatures in the fuel [4]. Owing to the complex nature of the problem, most thermal conductivity models for irradiated fuel are

60 empirically-based, with limited applicability to designs outside the experimental space for which data exists [5].

In previous research, empirical models are fitted to bulk measurements of the fuel thermal conductivity, due to the difficulty in measuring the thermal conductivity at the microstructural level. However, new optical micrographs of high burn-up fuel obtained at Idaho National Laboratory (INL) provide a means to evaluate the thermal conductivity of microstructures [6]. The optical micrographs can be reconstructed as finite element meshes, allowing the virtual measurement of the thermal conductivity.

In this work, the post irradiation micrographs and dimensions from fuels with burn-ups between 5.8-23.8% FIMA are used to develop finite element-based models for effective thermal conductivity of fuel at end of life. These finite element microstructural-based thermal conductivity models were then used to evaluate the prominent semi-empirical analytical models at burn-ups both within (5.8-6.7% FIMA) and well outside (21.3-23.7%FIMA) the data originally used to generate the existing analytical models.

4.3 Background

Analytical and computational modeling approaches have been taken to attempt to understand and predict the behavior of high burn-up fuel. The two most widely used analytical models derived from empirical measurements are the modified Duriez-Nuclear Fuel Industries (NFI) model, and the Duriez-Lucuta model [5, 7-9]. The modified Duriez-NFI model is used in FRAPCON-3, the standard code for modeling high burn-up fuel performance for NRC reactor licensing [5], while the Duriez-Lucuta model is recommended by Carbajo et al. for high burn-up MOX [10]. The Duriez-NFI model uses measurements from un-irradiated MOX fuel pellets and burn-up degradation functions based on UO2 data to empirically predict the thermal conductivity of MOX fuel pellets in LWRs up to 62 GWd/tHM [5, 8]. The model is strictly empirical and has only been validated for modeling of fuel for in the tested regime [5]. Additionally, the use of

UO2 data for the burn-up degradation of MOX fuel conductibvity results in an uncertainty of ±15-20% [5, 8]. The Duriez-NFI model is shown in equations 4.1-4.4.

61 (4.1)

(4.2)

(4.3)

(4.4)

The Duriez-Lucuta model utilizes the equation for unirradiated MOX as a function of temperature and plutonium content developed by Duriez et al. (4.5)

(4.5)

Where ko is unirradiated thermal conductivity, x is the shift from stoichiometry, and T is temperature in kelvin.

The Duriez unirradiated thermal conductivity is then modified by a series of multiplier: dissolved fission products (Fd), porosity (Fb), precipitated fission products (Fp) and radiation damage (Fr) as outlined in detail by Lucuta et al.[7, 11] and shown in equations 4.6-4.10.

(4.6)

(4.7)

(4.8)

(4.9)

(4.10)

Where β is the burn-up in % FIMA, T is temperature in kelvin, and ρ is the percent porosity.

The dissolved fission product term is based on the measured degradation of fission products in SIMFUEL, and takes into account the effect of all fission products that are incorporated into the fluorite matrix, including fission gas atoms[9]. The dissolved fission products reduce the conductivity in the phonon-transport regime by acting as phonon scattering sites [39]. The precipitated fission products term, Fp, is based the assumption of metallic precipitates forming within the grains and on grain boundaries and is treated using a modified Klemens’ perturbation factor to incorporate increased precipitates as a function of burn-up[9, 51]. A key assumption in the calculation of both precipitated and dissolved fission products is the chemical state that the fission products are in, which the model uses unirradiated SIMFUEL to estimate; however, extensive chemical characterization of irradiated fuel would eliminate the assumptions of using simulated fuel from the model. The porosity term, Fb, is the Maxwell-Eucken equation effect of porosity where the pores have much lower conductivity than the matrix phase. The thermal transport within the pores is assumed to be via radiation only, which may be conservative based on the high pressures thought to be present in the pores of the HBS regions[7, 9, 52] Lucuta acknowledges that the Fb term is a crude simplification of the complex situation of porosities effect on thermal conductivity in oxide fuel; however, for simplicity it is utilized. Since porosity is inhomogeneous throughout the pellets and evolves with burn-up the Fb term is typically only used to account for initial pellet porosity[50]. The discrete modeling of porosity including the true shape and size distribution performed in this work provides direct comparison of this simplification to real microstructures. The radiation damage term is derived from an empirical fit

63 to reduction in thermal conductivity of UO2 early in life due to radiation damage. There is no dependence on burn-up since the effect of radiation damage saturated early in life for oxide fuel [9, 50]

The second approach to model the thermal conductivity of irradiated oxide fuel is to use finite element to model the impact of various parameters such as porosity, precipitates, and microstructure [12]. Computer-based finite element modeling is maturing based on the increasing availability of computing power/capability [13]. Bakker et al. performed a series of 2D and 3D finite element studies to determine the effect of radiation heat transfer across pores on the overall thermal conductivity of irradiated UO2 fuel [14, 15]. They then compared the results to various analytical models for similar phenomena [15]. The finite element models were in agreement with accepted analytical models; however, both the finite element models created/used by Bakker et al. and the analytical models that they compared their results to are based on idealized microstructures. Thus, these results are of limited applicability to real microstructures [14, 15]. Realizing the shortcomings of these idealized models, modelers, including Bakker et al., have begun to incorporate more realistic microstructure and phase information into models [12, 16]. Historically, this was a time consuming process, as real microstructures had to be manually digitized to create meshes for importation into finite element solvers [12, 14, 17].

The need for a more automated means by which to create mesh models of real microstructures gave rise to OOF2 (Object Oriented Finite element analysis version 2), a freeware program created and supported by the National Institute of Standards and Technology (NIST)[18, 19]. Complex real micrographs with multiple phases can be imported into OOF2 and then converted into computational meshes for finite element modeling [19]. Utilizing microstructure-based meshes versus homogenized unit cells or meshes based off of idealized microstructures greatly increases the accuracy of finite element models for heat transport across microstructures [20, 21]. Additionally, microstructure-based models of complex microstructures provide better agreement with experimental data for thermal and mechanical properties than either idealized finite element or analytical models [19-28]. The development of a more fundamentally-based model will allow for the design of future fuels with reduced testing requirements [7, 29, 30].

64 4.4 Sample History/Background

The fuel samples analyzed in this work were irradiated in the Fast Flux Test Facility (FFTF) in the mid-1980’s to early 1990’s. The fuel samples came from the FO-22 and ACO-32 fuel assemblies, which contain annular MOX fuel pellets with HT-9 cladding. Optical micrographs from four fuel cross-sections were analyzed and modeled. The analyzed sections were sectioned from the mid-plane and ¾ up the fuel column and had a burn-ups ranging from 5.58-23.7% FIMA. A summary of the irradiation history and sample details is found in Table 4.1. More detailed irradiation history has been previously submitted by Teague et al. [6].

4.5 Microstructural Modeling

The methodology utilized for constructing and running the microstructural models along with the material models that were used are included in this section. The results of these models are then given and compared to semi-empirical models.

4.5.1 OOF Microstructure Reconstruction

The radial micrographs were broken into two to three pieces based on microstructural feature. The lower burn-up FO-2 samples were broken into columnar and equiax/edge regions, while the ACO-3 micrographs were broken into three regions: columnar, equiax, and rim.

Table 4.1. Irradiation history of fuel samples. Sample ID FO-2A FO-2B ACO-3A ACO-3B Distance from 40.1 68.9 40.1 68.9 Bottom of Fuel Column (cm) Burn-Up 6.7 5.8 23.7 21.3 (%FIMA) EOL LHGR 36 33 21 19 (kW/m) Coolant Temp (K) 633 633 633 633 Coolant Flow rate 114 114 105 105 (g/s)

2 The significance/meaning of the assembly identifiers FO-2 and ACO-3 have not been located in the historical literature. It is possible that they were randomly assigned identifiers.

65 Figure 4.1 illustrates the selection of microstructures from the radial micrograph for ACO-3A, while Figure 4.2 shows the rest of the optical micrographs used for the modeling. These sections were then imported into OOF2 to generate finite element meshes, using the basic process outlined in Figure 4.3. Initially, a uniform mesh made of elements (in this example, triangular elements) is overlaid on the micrograph (Figure 4.3a) followed by annealing/refinement steps. The goal of the annealing steps is to increase the material homogeneity of each element, defined in OOF2 as [19]:

(4.11)

(4.12)

(4.13)

where α is a tunable parameter between 0-1, T is the current element, ai(T) is the fraction of elements composed of pixel set i, N is the number of pixel categories, AT is the area of the current element and LT is the perimeter of the current element.

Figure 4.1. Radial cross-section of sample ACO-3A with subsections used for modeling marked.

Figure 4.2. Radial optical micrographs of ACO-3B, FO-2B, and FO-2B used for mesh generation.

Figure 4.3. Mesh creation in OOF2 [19].

67 The annealing steps are performed by a Monte Carlo algorithm where elements are moved at random and the changes are kept if the resulting element is more homogeneous than the previous element [19]. Figure 4.3b shows an example mesh after 10 annealing iterations. Elements whose E is greater than a specified value (in this case 0.3) are then divided in half (Figure 4.3c) and further annealing steps are performed (Figure 4.3d).

In order to increase the homogeneity of the mesh, more elements are required, which results in increased computational costs. A mesh refinement study was carried out and it was determined that increasing the homogeneity of the mesh above 97% changes the effective thermal conductivity by <5%; therefore, all microstructural meshes were refined to a minimum of 97% homogeneity. Further detail on the mesh refinement study can be found in Appendix B.

4.5.2 Microstructural Methods

The meshes generated via OOF2 were then imported into INL’s BISON fuel performance code for thermal analysis [1]. The 2D effective thermal conductivity of the microstructures in the radial direction was calculated as a function of temperature in a procedure outlined by Millet et al. [30]. In this procedure the effective thermal conductivity is calculated by applying a constant temperature, Tb, to the bottom boundary and a test heat flux q=qt over the top boundary, as illustrated in Figure 4.4.The top boundary of the microstructure is the side closest to the coolant; which is the primary direction of heat flow in pellet nuclear fuel. The test flux, qt, was selected for each microstructure to obtain a temperature drop of 10 K or less across the microstructure. Periodic boundary conditions were applied to the sides of the structure. The steady-state temperature gradient in the microstructure was determined by solving the steady-state heat conduction equation

. (4.14)

The effective thermal conductivity was determined using the following equations,

(4.15)

(4.16)

68 Where Keff is the effective thermal conductivity, is the average temperature across the top boundary and l is the side length of the microstructure.

The Duriez-Lucuta model was utilized as described above for the thermal conductivity of the fuel phase, with the multipliers for precipitated fission products and porosity omitted, as they are directly represented by the microstructure mesh. The observed bright white precipitates were all assumed to be metallic based on the light reflecting properties of metals versus ceramic precipitates. Previous investigators who have observed ceramic precipitates describe them as a grey phase, due to their dull appearance [3, 31]. Yamanaka et al. studied simulated metallic precipitates with compositions over the range that have been observed in fast reactor fuel, the measured thermal conductivities of the various alloys were extremely close and within measurement error; therefore, a single temperature thermal conductivity relationship was applied to all metallic precipitates, Eqn. 17.[32].

Figure 4.4. Effective thermal conductivity model, red is metallic precipitates, yellow porosity, and fuel is light blue, enlarged region of mesh is shown to right to high light varying element density to capture microstructure detail. The effective thermal conductivity of the microstructure is calculated using equation 4.6.

69 Due to the inability to distinguish ceramic precipitates that may have been present from the fuel matrix, their effect on the effective thermal conductivity was not considered in this evaluation.

(4.17)

Where km is the thermal conductivity of metallic precipitates and T is temperature in kelvin. The pores were assigned the temperature dependent thermal conductivity of a Xe-Kr-He mixture, the thermal conductivities measured from Saxena et al. were used for Xe, Kr, and He, while the mixture of gases was treated using the Wassilijewa-Maxon-Saxena equations (Eqns 18- 19) [33, 34], where the gas mixture was based on gas analysis performed on the puncture pins. FO-2 gas mixture was 14.4% He, 6.2% Kr, 79.4% Xe, while the ACO-3 gas mixture was 7.6% He, 6.4% Kr, and 86.0% Xe.

(4.18)

(4.19)

Where kmix is thermal conductivity of mixture of monoatomic gases, ki and kk are conductivities of component gases, xi and xk are fractions of gases, and Mi and Mk are molecular weights of component gases. Perfect contact was assumed between phases and pores. Each microstructure model was run at temperatures between 500-3100 K and a polynomial fit of the effective thermal conductivity of the microstructures as a function of temperature was empirically derived, shown in Table 4.2. These 2D effective thermal conductivities provide a lower conservative bound to the thermal conductivities of the microstructures, since a pore in a single plane acts as an infinitely tall pore with no means of heat to bypass it, which is conservative [12, 14]. Bakker et al. developed correlations for converting idealized 2D finite element based conductivities to 3D conductivities [12, 14]. However, due to the highly complex microstructure and three phases present in the studied samples there is not an adequate understanding of the 3D structure of these materials and idealized conversion factors for the for difference between 2D and 3D thermal conductivities were not applied.

70 Table 4.2. Polynomial fits to effective thermal conductivity for microstructures of the form 4 3 2 keff=AT +BT +CT +DT+E, where keff is effective thermal conductivity in W/m*K and T is temperature in K. A B C D E FO-2A Columnar -3.28E-14 2.80E-10 -4.24E-7 -4.63E-04 2.11 Edge -4.26E-14 3.58E-10 -5.10E-07 -6.97E-04 2.76 FO-2B Columnar -3.78E-14 3.16E-10 -4.11E-07 -7.68E-04 2.70 Edge -4.10E-14 3.40E-10 -4.51E-07 -7.89E-04 2.81 ACO-3A Columnar -4.52E-14 4.04E-10 -8.48E-07 2.09E-04 1.66 Equiax -4.80E-14 4.29E-10 -9.22E-07 3.13E-04 1.62 Rim -4.46E-14 3.71E-10 -7.96E-07 2.66E-04 1.40 ACO-3B Columnar -3.26E-14 2.93E-10 -6.60E-07 3.33E-04 1.00 Equiax -4.41E-14 3.94E-10 -8.54E-07 3.03E-04 1.48 Rim -4.16E-14 3.68E-10 -7.77E-07 2.12E-04 1.47

4.5.3 Microstructural Results

The effective thermal conductivity as a function of temperature calculated using the finite element based microstructural models was compared to the Duriez-Lucuta and Duriez-NFI models for sample FO-2A and FO-2B, as shown in Figure 4.5. The modified Duriez-Lucuta model thermal conductivity incorporating only the correction factors for dissolved fission products and radiation damage, which was used as the thermal conductivity of the fuel phase, is shown for reference.

The effective thermal conductivities of the columnar region in both FO-2A and FO-2B were slightly lower than that of the edge/equiax region. The lower thermal conductivity in the columnar region is due to the higher porosity in the microstructures as seen in Figure 4.2.

Figure 4.5. Graphs of effective thermal conductivity of microstructures in a) FO-2A and b) FO-2B compared to analytical models.

Both the edge and columnar thermal conductivities of FO-2A and FO-2B are slightly lower than the values predicted by the full Duriez-Lucuta model but are within 20%, which is the reported error in the model when applied to MOX [7, 10].For temperatures up to 1600K in FO-2A, the modified Duriez-NFI model is lower than both the edge and columnar regions; above 1600K the edge and columnar thermal conductivities are significantly lower than the values predicted by Duriez-NFI. FO-2B shows a similar trend for the edge conductivity; however, the columnar conductivity is below the Duriez-NFI over the entire temperature range.

Figure 4.6 shows the finite element calculated effective thermal conductivities of the microstructures in ACO-3A and ACO-3B compared to those calculated using the Duriez-Lucuta and Duriez-NFI models. Again, the modified Duriez-Lucuta thermal conductivity is plotted for reference. The thermal conductivities from the finite element model for the equiax and columnar regions in ACO-3A are extremely close, while the rim region’s effective thermal conductivity is ~15% lower throughout the temperature range. The lower rim thermal conductivity is due to the significantly higher porosity in the rim structure (~20% in rim versus ~12% in equiax and columnar region, as shown in Figure 4.1). Note that experimental results indicate that the high burn-up structure region of fuel has ~55% higher thermal conductivity than predicted by analytical models. This increase is proposed to be due to healing of irradiation damage and removal of dissolved fission products during the formation of the high burn-up structure [4]. Due to the limited data for this finding and significant difference between the fuel tested in [3] and

72 the fuel under study here, this enhancement was not considered in this work. Finite element thermal conductivities for ACO-3A are above those predicted by Duriez-NFI for temperatures up to ~1500-1800K, above which the Duriez-NFI values increase rapidly. The Duriez-Lucuta predicted values for ACO-3A is within 10% of the values calculated for the equiax and columnar regions, while the rim region is ~10-20% lower than that predicted by Duriez-Lucuta.

In ACO-3B, the finite element calculated effective thermal conductivities of the rim and equiax regions are very close; while, the columnar region is ~20-25% lower. The lower effective thermal conductivity in the columnar region is due to the higher porosity in the columnar region compared to the rim and equiax regions (~23% in columnar, versus ~12% and 15% in the rim and equiax regions respectively, Figure 4.2). The ACO-3B rim and equiax thermal conductivities show a similar trend as the equiax and columnar regions of ACO-3A when compared to the Duriez-NFI model. For temperatures up to 1500K the finite element -calculated values are above Duriez-NFI values, but then become significantly lower by 2000K. The finite element -calculated columnar thermal conductivity is lower than the Duriez-NFI model values over the entire temperature range studied.

Figure 4.6. Graphs of effective thermal conductivity of microstructure in a) ACO-3A and b) ACO-3B compared to analytical models.

The finite element conductivities of the rim, equiax, and columnar regions are all below that calculated using Duriez-Lucuta over the temperature range. The rim and equiax region conductivities are 15-20% below the Duriez-Lucuta values, while the columnar region conductivity is ~35-40% lower than the Duriez-Lucuta predicted value.

73 4.5.4 Microstructural Discussion

Overall, the Duriez-Lucuta has the closest agreement to the microstructure-based finite element models developed here, with its values being only 10-20% higher than the finite element -based values for the majority of samples. This agreement suggests that the Duriez-Lucuta terms defining the effect of porosity and dissolved fission products capture the same phenomena that are being modeled discretely in the finite element based models. Additionally the close agreement between the 2D FEM models developed here and the 3D bases analytical models suggests that the 3D component to thermal conductivity is not greater than the model uncertainty. The agreement at burn-ups below those at which the Duriez-Lucuta model was developed (up to 10% FIMA) is to be expected since the models were developed to match the available data; however, the agreement at burn-ups over 20% FIMA is a significant finding. The agreement well outside the data set used for the model development seems to indicate that the degradation of thermal conductivity as a function of burn-up continues via the same mechanisms up to burn-ups of ~23% FIMA.

4.6 Pellet Scale Modeling

The methodology used for developing the pellet scale models are outlines in this section. The pellet scale models results run using both the microstructural based FEA fits and semi-empirical analytical models are presented and the impact of the various models on fuel centerline and surface temperatures is discussed.

4.6.1 Pellet Scale Methods

A tightly coupled thermomechanics simulation was conducted in order to evaluate the impact of the differences between the finite element based model developed here and the Duriez-NFI and the Duriez-Lucuta models on predictions of the centerline temperature at end of life (EOL) in a fuel pin. This engineering scale simulation was modified from the axisymmetric discrete-pellet fuel rodlet problem discussed in detail by Williamson et al. [1].

An example of the geometry and materials used for the FO-2 and ACO-3 pellets are shown in Figure 4.7. The fuel-clad gap, cladding thickness, pellet outer diameter, pellet inner diameter, and thickness of microstructure regions were determined using post-irradiation examination measurements of fuel cross-sections [6]. The temperature dependent thermal expansion proposed

74 by Carbajo et al. was used for the MOX fuel. The Young’s modulus and Poisson’s ratio of the fuel were assumed constant at 175 GPa and 0.276[35, 36]. Temperature dependent thermal conductivity and thermal expansion were assigned to the HT-9 after the work of Leibowitz et al. [37]. The Young’s modulus and Poisson’s ratios of the HT-9 were assumed constant at 178 GPa and 0.308[38].

The models were run using the modified Duriez-NFI model, the Duriez-Lucuta model, and the microstructural-based model developed in this work in order to compare the resulting temperature profiles.

For the FO-2 pellets, the gap between pellet and cladding was assigned a conductivity based on the experimentally determined fission gas composition, as discussed above. For the ACO-3, the gap was treated in two different ways: first as being open and filled with gas as describe above, and secondly as being filled with cesium molybdate (Cs2MoO4).

Figure 4.7. Geometry, materials, and typical mesh used for axisymmetric simulation of fuel pellet temperature profile.

The cesium molybdate was assigned a temperature-dependent thermal conductivity based on the work of Minato et al. [39]. Utilizing the end of life (EOL) linear heat generation rate of the fuel, a neutron heat source was applied to the pellet region, while a uniform convective boundary was applied to the clad surface to simulate heat transfer to flowing coolant. The

75 thermal boundary conditions used for the two FO-2 and ACO-3 pellets can be found in Table 4.1. The displacement boundary conditions for the fuel and the clad allow volumetric expansion, yet prevent rigid body motion.

4.6.2 Pellet Scale Results

The results from the comparative pellet-scale models for the FO-2 samples are summarized in Table 4.3. The highest centerline temperature for both FO-2A and FO-2B was obtained from the radially-dependent finite element based model developed in this work, followed by the Duriez-Lucuta model. The Duriez-NFI model resulted in the lowest fuel centerline temperatures. The centerline temperature for FO-2A ranges from 2622K for the Duriez-NFI model to 2740 K for the finite element model. The centerline temperatures for FO-2B ranged from 2779 K for Duriez-NFI to 2867 K for the finite element model. The fuel surface temperatures show a reverse trend, in that the highest fuel surface temperatures were given by Duriez-NFI and the lowest by the finite element models. The lower fuel surface temperatures given by the finite element model is due to a decreased gap size from increased thermal expansion. The increased heat transfer due to reduction in gap size overwhelms the lower thermal conductivity at the edge of the pellet to result in lower fuel surface temperature in the finite element models.

The radial temperature profiles in the FO-2 pellets both show a clear transition from the columnar to the edge region, which is in agreement with what would be expected based on the calculated temperature profiles (see Figure 8). The centerline temperatures are all in excess of the minimum temperature for columnar grain formation, ~2073 K [3]. The columnar regions stop at a radius ratio r/ro of 0.75 and 0.7 for FO-2A and FO-2B, respectively. The temperature at r/ro= 0.75 is 2007 K for FO-2A, which is in agreement with the point at which columnar grain growth would stop. The temperature at r/ro= 0.7 in FO-2B is 2375K, which is significantly above the point at which columnar grain growth should occur.

The temperature does not drop down below 2073K until r/ro= 0.87. This finding along with the significantly higher (~400 K) fuel surface temperature in FO-2B over FO-2A indicates that the finite element based pellet model for FO-2B is not capturing an important phenomena. The primary difference between FO-2A and FO-2B pellet models is the gap size 70 and 91μm

76 respectively. One possible explanation described further below, is that the gap is either partially or completely filled with solid fission products with a higher thermal conductivity than the gas.

Table 4.3. Comparison of fuel centerline and surface temperatures in FO-2 samples from pellet scale modeling using Duriez-NFI, Duriez-Lucuta, and radial dependent finite element models. Fuel Fuel Centerline Surface (K) (K) FO-2A Duriez-NFI 2622 1580 Duriez-Lucuta 2680 1546 FEA Model 2740 1456 FO-2B Duriez-NFI 2779 1921 Duriez-Lucuta 2839 1867 FEA Model 2876 1826

Figure 4.8. Temperature profile for FO-2A and FO-2B calculated using the finite element model.

The ACO-3A and B micrographs show a large gap, ~200 μm, which is over twice as large as the as-fabricated, 95 μm, fuel cladding gap. Due to the high burn-up of these samples and previously published PIE of similar fuel it was suspected that the gap is filled with solid fission products, primarily cesium molybdate often referred to as joint oxyde gaine (JOG)[6, 17, 40-42].

77 Due to the hydroscopic nature of cesium molybdate and the water-based preparation techniques used to prepare the samples, the JOG layer was likely not retained during preparation. To test the assumption that JOG filled the measured gap, the ACO-3 pellet models were run with both mixed gas and cesium molybdate in the gap, as shown in Figure 4.9. The thermal profiles of the pellets show that the centerline temperature with a gas-filled gap for both pellets is ~3500K, well in excess of the melting temperature of MOX fuel, 3083 K[3]. The same models run with cesium molybdate in the gap have significantly lower centerline temperatures of 2153K and 2101K for ACO-3A and ACO-3B, respectively. The micrographs show no signs of fuel melting; therefore, the assumption of the gap being filled with JOG is further supported by the thermal modeling.

The ACO-3 pellet models were then run with cesium molybdate in the gap using the three thermal conductivity models being evaluated here: Duriez-NFI, Duriez-Lucuta, and finite element models. The fuel centerline and fuel surface temperature calculated using the three models for pellets ACO-3A and ACO-3B can be found in Table 4.4. The centerline temperatures calculated by the ACO-3A model ranged from 2068 K for the Duriez-NFI to 2186 K for the Duriez-Lucuta.

Figure 4.9. Comparison temperature profiles in pellets ACO-3A (left) and ACO-3B (right) with CS2 MoO4 filling the gap and with gas filled gap.

The centerline temperatures for ACO-3B ranged between 2009K from Duriez-Lucuta and 2139 K from finite element model. In the results from both the FO-2 and ACO-3 pellets, the model with the lowest thermal conductivity over the relevant temperature range results in the

78 highest centerline temperature, as expected. The fuel surface temperatures for both pellets, regardless of the model used for thermal conductivity, were extremely close (7 degree spread for ACO-3A and 6 degree spread for ACO-3B), which is in stark contrast with the behavior seen in the FO-2 pellets. This difference is due to the gap being filled with cesium molybdate in the ACO-3 pellets, which has a thermal conductivity approximately one order of magnitude larger than that of the gas mixture. Due to this higher thermal conductivity, the gap size difference due to the thermal expansion of the fuel has very little effect on the fuel surface temperature [34, 39].

The calculated temperature profiles in the ACO-3 pellets, using any of the three models, are in agreement with the metallographic results. The centerline temperatures of ~2000-2200 K are close to or just above the temperature at which columnar grains form, and as these are end of life temperatures, the fuel would have seen higher temperature earlier during irradiation life. The edge of both ACO-3A and ACO-3B show the classic high burn-up rim structure which has a upper temperature limit of ~1273 K, above which it does not form. The calculated fuel surface temperatures of ~1146-1177 K are below this bound and in agreement the metallographic findings.

Table 4.4. Comparison of fuel centerline and surface temperature

Fuel Fuel Centerline Surface (K) (K) ACO-3A Duriez-NFI 2068 1177 Duriez-Lucuta 2186 1170 FEA Model 2163 1171 ACO-3B Duriez-NFI 2101 1148 Duriez-Lucuta 2009 1152 FEA Model 2139 1146

4.7 Conclusions

In this work, experimentally derived microstructures from irradiated fuel were successfully transformed into finite element meshes for thermal analysis. These microstructural meshes were

79 used to develop radial and temperature dependent models for the thermal conductivity of the studied pellets. The results were compared with the Duriez-NFI and Duriez-Lucuta analytical models. The Duriez-Lucuta model has the closest agreement with the finite element models developed here, with thermal conductivity values only 10-20% higher. The Duriez-Lucuta model, despite being based on low burn-up data for porosity and precipitated fission products, agrees with explicitly modeled porosity and metallic fission products in fuel microstructure in fuel with burn-ups up to 23.7% FIMA.

In addition to the microstructure calculations, thermal profiles were calculated with tightly coupled thermomechanics simulations for the pellets using pellet-scale thermal models and EOL irradiation conditions. The finite element-based thermal models, the Duriez-NFI, and Duriez-Lucuta models all produced centerline and surface fuel temperatures within 100 K of each other, and were consistent with metallographic findings. In addition, these thermal profile calculations provided evidence supporting the hypothesis that the experimentally observed gap in higher burn-up samples (21.3 and 23.7% FIMA) was filled with cesium molybdate.

4.8 Acknowledgements

The authors would like to thank Doug Porter and John Lambert for the extensive discussions on the data and lessons in oxide fuel performance. This work was funded by the Department of Energy Fuel Cycle and Research Development program and the INL Laboratory Directed Research & Development (LDRD) Program. This manuscript has been authored by Battelle Energy Alliance, LLC under Contract No DE-AC07-05ID14517 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United Sates Government retains a nonexclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow other to do so, for the United States Government purposes.

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83 CHAPTER 5

GENERAL CONCLUSION

5.1 Conclusions

The understanding of the evolution of microstructure, crystal structure, and chemistry in mixed oxide fuel was increased by extensive characterization of irradiated fuel with burn-up between 3-24% FIMA. Optical microscopy of the samples revealed that the fuel-cladding gap was found to close significantly in samples with burn-ups below 7-9% FIMA due to fuel swelling; while the samples with burn-ups in excess of 7-9% FIMA showed a reopening of the fuel-cladding gap and evidence of joint oxide gaine formation. The highest burn-up samples (21.3 and 23.7% FIMA) were found to have a distinct high burn-up structure region at the periphery of the pellets. The region was ~500 μm thick, which is 3-5 times thicker than the high burn-up regions observed in light water reactor fuel pellets. More detailed characterization was performed on the 6.7% FIMA burn-up sample.

Dual column FIB/SEM was successfully used, for the first time, to prepare high quality TEM and cube EBSD/EDS samples from high burn-up MOX fuel. The Utilization of the FIB for TEM sample preparation resulted in significantly smaller, by mass, TEM sample compared to traditional TEM 3 mm disc samples. The dose of the prepared TEM samples was 3.5x10-8R/hr compared to 1.1R/hr for traditional samples. This reduction in dose rate makes working with the samples significantly safer. TEM characterization found that the rim region of the fuel pellet had a ~2.5x higher dislocation density than that of the sample from the mid-radius due to the lower irradiation temperature at the rim. Characterization of the fuel cubes via EBSD and EDS showed that the sample from near the central void had large inter-granular metal precipitates, while the sample from the rim contained small inter- and intra-granular precipitates. EBSD characterization of irradiated fuel, especially the HBS region, has the potential to provide critical data for understanding the formation of the structure. The orientation of the grains and the angle of grain boundaries can indicate what mechanisms forms the small grains in the HBS region. Previously only TEM could be used to measure grain boundary angles in irradiated fuel, unfortunately TEM provides a very small sample set of grain boundaries making general conclusions difficult. The larger sample size available using EBSD characterization will help to resolve conflicting grain boundary angle measurements made via TEM.

84 The ability to obtain 3D microstructure data from irradiated fuel will revolutionize the ability to accurately model the thermal transport in fuel. Historically the microstructure of fuel has only been studied in one dimension due to experimental limitations in obtaining 3D data, the application of FIB serial sectioning to these materials will allow for key questions as to the correlation between 2D and 3D microstructures in irradiated fuel to be made. Since the first application of these techniques in this PhD work, a number of researchers have begun to use the same techniques to study a wide range of irradiated materials and fuel systems.

The experimental characterization of the high burn-up fuel samples were used to develop microstructural based models for the effective thermal conductivity of the studied pellets. The finite-element based models were compared with the Duriez-NFI and Duriez-Lucuta analytical models. The Duriez-Lucuta was found to be the closest in agreement with the developed finite- element based models, with values 10-20% higher. The agreement between Duriez-Lucuta and finite-element based models at burn-up well in excess of where the Duriez-Lucuta model was develop (23.7% FIMA verse 10% FIMA) indicates the same degradation in burn-up trends are present at the increased burn-up range. The applicability of Duriez-Lucuta to high burn-up samples provided confidence that these semi-empirical models are robust enough to apply to higher burn-up fuels, though experimental measurements of thermal conductivity would still be required to validate them for design use.

End of life thermal profiles were calculated for the pellets using pellet scale thermal models and EOL irradiation conditions. The finite-element based models, Duriez-NFI, and Duriez-Lucuta models all produced centerline and surface fuel temperatures within 100 K of each other, validating the applicability of microstructure based thermal conductivity models to pellet scale. The close agreement between the microstructure based models and analytical models, provides confidence in the microstructure based approach. This agreement could allow for thermal scoping design work of significantly different fuel designs and materials which is currently not capable of being performed with the analytical models. Thermal profile calculations of the high burn-up (21.3 and 23.7% FIMA) samples were run with both a filled and open gap. The results clearly show that the gap was filled with cesium molybdate.

85 This PhD work successfully added to understanding of the evolution of microstructure and chemistry in mixed oxide fuel, while demonstrating the application of advanced characterization techniques, FIB TEM and EBSD, to high radiation samples. The experimental data was then successfully used to generate effective thermal conductivity models, and pellet scale models for calculation of thermal profiles.

5.2 Future Work

Follow on work to this project should include advanced characterization such as EBSD, EDS, and TEM of the remaining fuel pellets, that had only optical microscopy performed. Analysis of these samples will allow for further insight into chemical and grain evolution as function of burn-up and irradiation temperature. EBSD and TEM of the high burn-up structure areas of the 21.3 and 23.7% FIMA samples could provide important information about the formation of the structure, and comparisons between the grain sizes and orientation of the high burn-up structure in fast reactor fuel and light water reactor fuel. Another key analysis that would be useful to furthering this study would be utilization of a surface thermal conductivity measurement technique such as scanning thermal diffusivity microscope (STDM). The STDM can provide the thermal diffusivity along the radius of a fuel pellet with a 50-100 micron spot size. This measurement could be used to directly validate the thermal conductivity models developed in this thesis.

Future modeling efforts should include further examination into the potential increase in fuel matrix thermal conductivity in the rim regions due to healing of radiation damage and removal of dissolved fission products. Additionally further examination as to the effect of different heat transfer mechanism such as convection over the pores in the rim structure due to their high pressure, and its impact on overall thermal performance.

86 Appendix A

Permission to include Papers from Co-Authors

Figure A-1: Permission to publish submitted articles.

Figure A-1. Permission from Douglas Porter for publication.

Figure A-2. Permission from Brandon Miller for publication.

Figure A-3. Permission from Michael Tonks for publication.

Figure A-4. Permission from Stephen Novascone for publication.

Appendix B

Mesh Sensitivity Study

In order to determine the sensitivity of the effective thermal conductivity calculations outlines in section 4.5 to the homogeneity of the OOF2 generated meshes, a series of meshes with varying homogeneities were tested. This process was conducted for all microstructures modeled; however, for brevity only one example is outline here to show the process. Figure B-1 shows the micrograph section from the rim region of ACO-3A. OOF2 was used to generate four meshes with homogeneities of 94, 97, and 99%. These meshes are shown in Figures B-2-B4, and their properties outlined in Table B-1. The meshes were then run using the modeling methods outlined in section 4.5 to calculate the effective thermal conductivity of the microstructure at 1000 K. The mesh with homogeneity of 97% showed a 7.5% difference in thermal conductivity versus the 94% homogeneity mesh. The mesh with homogeneity of 99% only showed a 0.8% difference than the 97% homogeneity mesh, despite having three times as many elements. As tradeoff between accuracy and computing cost, a cut off of 5% difference was selected. Therefore, the mesh was refined until further refinement resulted in less than 5% difference in the calculated value. For all of the microstructures studied a 97% homogeneity level was determined to be sufficient to reduce the mesh effect to below 5%.

Figure B-1. Micrograph from rim region of ACO-3A.

Figure B-2. Mesh of rim region in ACO-3A with homogeneity of 94%. Blue is fuel, yellow porosity, and red is metal precipitates.

Figure B-3. Mesh of rim region in ACO-3A with homogeneity of 97%. Blue is fuel, yellow porosity, and red is metal precipitates.

Figure B-4. Mesh of rim region in ACO-3A with homogeneity of 99%. Blue is fuel, yellow porosity, and red is metal precipitates.

Table B-1. Properties of the tested meshes and the calculated effective thermal conductivity of each mesh at 1000 K. Homogeneity Number of Number of Effective Thermal Index Elements Nodes Conductivity at 1000 K(W/m*K) Mesh94 93.84 8104 8129 1.13 Mesh97 97.04 20020 15442 1.23 Mesh99 99.87 85009 56110 1.24

93 Appendix C

Nomenclature and Acronyms

ACO-3-Sub-assembly identifier for fuel with peak burn-up of 24.7% FIMA Burn-up-measure of how much of the fuel has been used or burned, has numerous units BOL (Beginning of Life)-conditions at start of irradiation of fuel BISON-Fuel performance code developed at INL Central Void-void in center of fuel pellets, it can either be present from fabrication, or form during irradiation CDE (Core Demonstration Experiments)-series of experiments carried out in the 1980’s and 1990’s to demonstrate the viability of high burn-up mixed oxide fuel EBSD (Electron backscatter diffraction)-characterization technique used to characterize crystal structure and orientation of polished samples EDS (Energy dispersive spectroscopy)-characterization technique used to determine elemental composition of a material EFPD (Effective full power days)-measure of how long a specimen was irradiated, due to irregular power cycles it is often normalized to full power days EOL (End of Life)-conditions present at end of irradiation of fuel FCCI (Fuel cladding chemical interaction)-chemical interaction between the fuel and cladding FCMI (Fuel cladding mechanical interaction)-mechanical interaction between fuel and cladding, i.e. straining of cladding due to pressure from fuel swelling FEA (Finite Element Analysis)-analysis method that used finite elements to solve differential equations FFTF (Fast Flux Test Facility)-fast test reactor located at Hanford, shut down in early 1990’s. FIB (Focused ion beam)-instrument which used a focused beam of Ga ions to prepare microscale samples FIMA (Fissions per Initial Metal Atom)-a measure of burn-up or depletion in a fuel Fission Products-elements generated during the fission process FO-2-sub-assembly identifier for fuel with peak burn-up of 6.7% FIMA GWd/tHM (Gigawatt day per tonne heavy metal)-unit of burn-up, typically used by industry

94 HBRP (High Burn-up Rim Project)-experimental campaign conducted to understand HBS formation HBS (High Burn-up Structure)-structure characterized by small sub grains and large porosity HFEF (Hot Fuel Examination Facility)-hot cell facility at INL that is capable of working with high radioactivity samples JOG (Joint Oxide Gain)-solid phase found in between fuel and cladding in high burn-up oxide fuel pins LHGR (Linear Heat Generation Rate)-measure of amount of power generated per unit length in fuel column LWR (Light water reactor)-thermal reactors that are cooled with light or normal water, all commercial reactors in US are LWR’s

MOX (Mixed Oxide Fuel)-uranium plutonium oxide, (U,Pu)O2 NFIR (Nuclear Fuel Industry Research)-Japanese industry consortium for studying fuel performance NRC (Nuclear Regulatory Commission)-Commission that regulated nuclear industry in US NIST (National Institute of Standards and Technology) OOF2 (Object Oriented Finite Element Analysis)-software developed by NIST to convert microstructures into finite element meshes SAFE-fuel performance code developed in 1990’s at Argonne National Laboratory-West SFR (Sodium fast reactor) TEM (Transmission Electron Microscopy)-characterization technique for looking at electron transparent samples, provide crystal structure and defect data TREAT (Transient Reactor Test Facility)-transient testing reactor at INL